I like Automatic Labguage Growth schools like the Thai school, and Dreaming Spanish, because they focus on a lot of comprehensible input lessons for beginner to intermediate learners. I think comprehensible input lessons are great!
They use pictures and gestures to make a language understabdable ENTIRELY in the language, so a student can learn entirely IN their target language (also why I love Nature Method textbooks). CI lessons are apso great if you have students with a variety of native languages, for example ESL classes. At the volunteer center I worked at, we exclusively did Comprhensible Input lessons until people could have full conversations in English, because explanations in English ftom the english speaking teachers were not useful until the students knew enough English. CI lessons worked well, we had speakers of 72 languages in the classes and it ensured everyone could understand lessons.
I also more or less agree that Krashen's comprehensible input hypothesis makes sense. The CI hypothesis was that when we learn through explanations like grammar books, we learn ABOUT the language, but we don't internalize the language. We internalize the language with many experiences in the language where we understand what's going on (comprehensible input). Which if you've learned a language... yeah... you can learn how to greet someone by memorizing in a book, but it won't become automatic until you've walked into class or a grocery store and been greeted in the target language - after a few times of that comprehensible input (understanding youre being greeted) you'll automatically be able to greet using those words in the language. Apply that to everything you do in a language: you might memorize a word list, but you won't acquire it (automatically understand and be able to use those words) until you've read them in a lot of reading material, or heard them in a lot of listening material or shows, in multiple situations you understand. This makes sense based on our experiences in our native language. We can look up "melancholic" at age 8 and learn the definition, but we'll need to read it several more times or hear people say it several more times to feel confident in what it means immediately when we encounter it and to use it ourselves.
As you can see, the input hypothesis includes room for translations and explanations if you want to use them. So a textbook maker could take the input hypothesis, and create an interesting graded reader for students to read alongside it and reinforce the word lists and explanations in the textbook with LOTS of comprehensible input. Students can learn ABOUT language with explanations (which can help make more experiences in the language comprehensible), then they learn to USE/UNDERSTAND the language with comprehensible input.
Many regular "learning to read" programs took this idea and ran with it: providing lots of reading material for readers at 98% comprehension for them is a strategy to improve reading level. Because at 98% (lowest being 90-95% depending on the study) comprehension of words, its very easy to guess the meaning of the remaining words from context, and then repeated context you understand (comprehensible input) internalizes those words, and then the level of what you can read goes up. I remember learning to read in my native language and yeah that's pretty much what happened. I learned to read in French and Chinese and yeah, that's what happened in my learning to read progression.
At the early stages of learning to read, teachers provide vocabulary lists for class, and assigned reading with word definitions (look at any textbook for any subject and see history, science, math, literature reading assignment definitions etc). At the early stages of French and Chinese I looked a LOT of words up to make reading material more comprehensible, then learned words fully by reading them in contexts I understood a LOT. That's also what happened in my native language English, I looked up definitions of stuff in school, and read assignments to learn the words fully, and in my free time read gradually more and more difficult books that were all likely ~95-98% comprehensible to me. As you know more words, what's comprehensible percentage wise goes up, and you can learn MORE stuff directly from context, and repetition in context, so you no longer need to use dictionaries and explanations (unless you choose - which many people keep doing sometimes, into adulthood).
So yeah, to me Krashen's comprehensible input hypothesis is easily compatible with how we learn our native languages, and all the languages we will study. The role of explicit study to Krashen, was either to make more experiences comprehensible (so we can fully learn the words in many comprehensible experience's context), or to build an internal monitor. Our internal monitor would help us answer tests, and check our own production skills.
Which again, matches fine with how we learn our native language. We LEARN spelling, we LEARN grammar in school. We know most of it before we get to school, but learning to perfect our grammar is a 10+ year effort in school - every time a teacher marks us down and corrects our spelling or grammar in an essay. According to the comprehensible input hypothesis, we dont truly become able to "naturally" use the grammar we struggle with until we have encountered it enough in context we understand, so extensive reading helps with grammar production (and explicit study to NOTICE the grammar, and understand what it's doing if we had previously thought it meant something else). But until we can naturally acquire grammar to the degree of producing it correctly, our internal monitor (built from years of school grammar and teachers correcting our essays) kicks in and can help us identify mistakes we made in our own writing. Or speaking (although we tend to make less mistakes in speaking since we don't have to spell as we speak, or use grammar punctuation marks, and written grammar has some additional challenges that dont come up in speaking).
So krashen's hypothesis, to me, seems compatible with how we learn all languages. It also explains why many people can become B2 and C1 speakers of languages they have explicitly sudied - their explicit study made more situations in the language more comprehensible, and then all that comprehensible input in the language understanding things in context helped them acquire the language, and they became able to use it to a high level. We know many classroom learners, who use translations and grammar explanations, learn languages to the B2 and C1+ levels. We know because every year people pass tests to prove it, they get jobs or go to college where they have yo speak the language daily in a variety of situations where they must be capable in using that language, and they succeed. I went to college with tons of people who learned English in school as children, through explicit teaching methods translation and explanations, who were doing fine in college classes entirely in English, in jobs entirely in English, in going clubbing and doing the fun stuff they wanted to do, in getting apartments and buying cars and paying bills in English.
ALG is not equivalent to Krashen's hypothesis. It's based on Brown's personal experiences. He thought people should learn entirely in the target language (which hey, I agree is a nice path to take, as extensive reading works similarly and works great for people in all languages for improving language skills) so he wanted entirely Comprehensible Input Lessons for students. He wanted students to avoid speaking for 1000+ hours, to produce a more natural pronunciation and to avoid making long term pronunciation mistakes based on the mistakes one could make as a beginner. He also advised not reading for around as long, to avoid mental pronunciations that could be wrong, so waiting to read until your listening skills and grasp of pronunciation sounds was solid. So it's an extreme position - nothing but watching and listening to Comprehensible Input Lessons (or comprehensible input Crosstalk lessons) until 1000+ hours. Then start speaking, and reading, and writing, once output feels natural. Brown believed "permanent damage" results if we explicitly study things such as look at translations and explanations, or even just think about the language analytically as we learn like trying to identify what's a noun or guess translations mentally, and read before we have a good mental model of the language's sounds. He felt this permanent damage would prevent us from ever reaching native speaker like level in a language. It creates a "ceiling" where learners will keep making fossilized mistakes caused from that permanent damage. He based this on his own ability in languages he learned and how when he "analyzed" a language he studied, he never was able to achieve as good of a level in that language, and continued making certain permanent errors.
I do not agree with some key points of ALG. Since ALG is just a theory Marvin Brown, 1 language teacher, had. It's not like his theory necessarily applies to anyone but his own lived experience. And possibly the ALG Thai school he ran, and for the students who followed ALG directions without deviating (and many do additional things, don't follow ALG precisely).
I think if there is "permanent damage" most people don't need to care. Many examples exist of people who reached B2 and C1 in languages, who did many things that Brown believes result in "permanent damage." So any damage does not seem to prevent you from reaching the highest standardized level of competence in a given language, any possible damage will not prevent you from becoming able to live and work successfully in a languahe. Including Brown as an example. He learned Thai, somewhat with methods he believed later caused "permanent damage." Despite this his Thai became good enough to work AS A LANGUAGE TEACHER so a very high level of competence in Thai, and to run a Thai Teaching School. His level of language ability allowed him to work and live in Thailand successfully and easily. Any permanent damage is only a major concern for the super picky perfectionists, like Brown the language teacher who likely aspired to be perfect at it. For the average person? If their goals are to live and work and go to school in a language, then any potential "permanent damage" will not stop them from reaching their goals.
I just do not think the things ALG says to avoid, actually matter all that much. Yes, I think waiting to speak and waiting to read COULD possibly produce better pronunciation in the long run. Yes, I think learning directly IN only the target language works (after all, I know extensive reading works, I know comprehensible input works, of course CI lessons work). So I think it's fine to go the ALG route if that gets you to learn, if it's the route you can stick with. It will work, to get you to your language goals, if you stick with it. Just check reddit.com/r/dreamingspanish to see all the success. (And all the success for people who did not follow ALG to the letter, as many people on r/dreamingspanish DID keep analyzing the language, keep taking explicit instruction courses, read early etc - and also had success).
My big issue with ALG is 1. It hasn't been tested much. ALG thai school and Dreaming Spanish are the only big pools of anecdotal experiences shared. And many of the students do NOT follow ALG to the letter, so many of the experiences shared confirm if Comprehensible Input lessons entirely IN the target language work (they do) and if they can get a student to B2 fluency (which it appears they can, when combined with adequate reading, and some speaking practice).
2. ALG is REALLY AGAINST any explicit instruction at any point. I think this is weird, and deviates from how children DO learn their native language. I see no reason why after 1500-2000 hours an ALG learner can't read or listen to grammar explanations IN THE TARGET LANGUAGE. Or talk to a tutor in the target language, and have the tutor grade their essays and mention any errors. We had all of that feedback in our native language. Why wouldn't we eventually want it in the target language, once our listening skills are that of a 10 year old native speaker? Native speakers receive grammar corrections, develop that "inner monitor" and it helps them correct their own mistakes until they've extensively read enough (or just done the situation enough in contexts they understood) that they've internalized the correct grammar point to use in writing/correct spelling. ALG basically avoids explicit instruction like the plague, and suggests to learners to just read or listen more. Which yes, does comply with Krashen's input hypothesis about how they'll eventually internalize the ability to use those language elements. But native speakers get corrections from teachers which "make" them understand what mistake they were doing sooner, and understanding will then make it more comprehensible in the future, making the student recognize and pick up that grammar point/spelling SOONER.
If an ALG student is blindly misunderstanding too/two/to for 4 years, before anyone mentions they are, couldn't that also cause "permanent damage"? Aka a mistake they keep making and fossilize, because for so long they'd been assuming too and to were the same word, they'd now have to unlearn that assumption and correct it with more exposure to it in contexts they understand (comprehensible input) now that they Correctly understand the words. Now we get to the issue of ALG believes there is no undoing/fixing "permanent damage."
Basically I think it's ridiculous to avoid explicit study IN THE TARGET LANGUAGE once you can competently listen and understand as well as 10-15 year old native speakers. I think at that point, explicit study will either HELP you as much as it helps native speaker kids, or at the least it wont cause any more "damage" than native speakers must get somehow in their normal course of schooling. To learn "like native speakers do" is to include explicit study eventually, in my opinion. It's ridiculous to pretend children dont ever get explicit instruction when they get YEARS of it.
(There's also the Output hypothesis in language learning. Which goes fine with Krashen's theory. We are corrected when speaking, or even just notice the other speaker is talking differently than us, and adjust our future speech to mirror the correct output. We practice outputting, and if the other person responds and successfully understood us then we internalize that understandable output and keep doing it. If the listener fails to understand us, we adjust our output in the hopes they will understand the adjustment - and we may base our adjustment on feedback they give us. Everyone who does Dreaming Spanish who ever talks to a tutor, language exchange, or just OTHER people is doing this. Because all speaking to other people, and then adjusting to be more easily understood, is compatible with the Output hypothesis. So even with ALG being entirely against explicit explanations, there is some "feedback" all people WILL GET when speaking with others, which will improve their output abilities over time. So even ALG speakers, as far as I can tell, eventually get some of the feedback that helps native speakers improve their own output as they grow up - simply talking with others).
So yeah. ALG has not been tested much. There's very few cases of people who really stuck with ALG theory from start to finish, although I love reading the experiences of those that do. From all other successful language learners, its clear that if "permanent damage" is real (and it might not be) then it doesn't prevent any learners from becoming competent for all ordinary life purposes in a language.
I dont think for normal purposes there's a reason a learner should strictly do ALG, over any other program. Do ALG if it's the program you can get yourself to stick with, or to test its claims as that's always interesting (to me anyway). But don't be afraid to study some other way.
As far as I can tell, many routes lead to the same achievement of "can do all things you want in the language."