Concerning Kakashi's skill as a teacher, I think a lot of the differing opinions how good he is is caused by differing ideas of what he's supposed to do. I've seen a lot of fanfic that "fixes" him and makes him more of a drill sergeant, having him decide how team 7 trains and what roles they take. A more true to canon take, I think, is that his job is to be more of team leader than having a master-apprentice kinda role. He teaches mission procedures, handing clients, and basically how to live as a ninja. He could probably give them some advice, about actual jutsu and stuff, maybe recommend certain teachers, make sure they aren't being irresponsible, etc. I think that he shouldn't have had to teach them tree walking, that being something they discover on their own, maybe with hints, but had to ignore subtlety due to the Wave mission. Like, the only other sensei that actually seems to be teaching their assigned student actual jutsu is Gai and Lee, everyone else, even close pairs like Asuma and Shikamaru, seems to be more like role models, or mentors. Idk if I'm explaining it right. TLDR Kakashi's a good sensei, his role in team 7 was never to be a drill sergeant/combat instructor, that role is fulfilled by master/apprentice relationships like Gai and Lee, and Sannin and team 7.
I may be wrong, but I don’t ever recall questioning Kakashi’s teaching skills. Heeeck, I’m one of his most ardent defenders 😊 lol. But I do also recognize his humanity.
I think Kakashi became a better sensei over time, but didn’t necessarily start out as a “good” sensei. But, before anyone jumps on me, that’s the nature of any job; especially one you never wanted. You learn by experience. A fresh, out of school, green neophyte on their first day ever on the job anywhere is not going to be as skilled as someone who’s been there 20 years, five years, or even just one year.
Kakashi, as a sensei, was just as confused as Naruto, Sakura, and Sasuke were as students. Dude was winging it, because there wasn’t any other way. He wasn’t expecting them to pass, nobody else ever passed his test before and he didn’t have enough faith in the Konoha ninja education system to believe they’d create a team of kids who could work as a team. He was only in school for a year, if that, so he didn’t know what those kids were learning. So, he wasn’t prepared. Or even lowkey, he may not have wanted them to pass because it meant, omg, I have to be responsible for other people, tiny other people, tiny other people with no skills.
In Anbu, yes, he was a captain, but that was different. Anbu was loneliness. Anbu was darkness. Anbu members were expected to be cold-blooded killers. And Anbu members typically weren’t 12 (he, Itachi, and Yamato/Tenzo were exceptions). He also didn’t have to teach; just train. Different ballgame.
Anyway, I digress, back to Team 7, one was the son of his sensei who he trying desperately to not remember because it hurt, not to mention the kid was feral (yeah, I said it, 12-year-old OG Naruto was feral - severe neglect will do that); another was the last member of his clan that was brutally murdered under the authority of the village, so that kid was a just a wee bit unhinged; and the third was the this little kunoichi that from his perspective probably shouldn’t have been in the ninja world in the first place because it was a cruel, cold, brutal life and she was “normal.” He didn’t know what to do with a normal kid - he was never one. In the end, he accepted the situation for what it was and learnt as much as he taught. And that’s the beauty of it - the teacher became the student and the students became the teacher.
It seems like the academy teaches bare basics - heck, he graduated in a year at age 5. I’m not downplaying his skills by any means, just stating the freak of nature that he is, completed years long training in just a fraction of that time and not sure if that says something about him or the education system - they weren’t prepared to work with prodigious kids and that says a lot. Yeah yeah yeah somebody will say they were at war, so they let the brat graduate. But that’s another post.
Anyway, that being said, I agree the academy should teach more. I strongly believe they should, at a bare minimum, learn their chakra nature while there. That seems like common sense. Just give out the litmus paper and test them and group them accordingly (I find it hard to believe that there are a bunch of shinobi going around not knowing what nature they have. Guess it would be based in your clan??). The basics of chakra control, water walking, tree climbing, etc… Makes you wonder what the heck they did teach them while there. I’m beginning to think it was just regular school and they learned some “cool ninja stuff” here and there - clones, substitution jutsu, taijutsu…
That being said, from what I garner, your clan is supposed to teach you their secrets and jutsu. Your sensei can’t do that. The school is supposed to teach you the basics 🤷🏽♀️. And your sensei is supposed to hone those skills. Take you on missions so you can learn in the field. Train your skills. Find your talents and strengths and enhance them.
As for Gai, Asuma, and Kurenai. I believe they all trained their students in different ways. My girl Kurenai doesn’t get much screen or page time, so you don’t know what she did or didn’t do or the hours she put in with them. Same for Asuma. You only get to see Gai’s team so much because Rock Lee is so awesome Gai is Kakashi’s rival, so more screen time by proxy. That’s not to say Asuma and Kurenai didn’t spend hours upon hours training their squads. Which I believe they did because at the end of the day, the K12 kicked butt and that required intensive training. Remember, all because you don’t see it happening, doesn’t mean it didn’t. They’re all amazing sensei in their own right. If you think about it, all those kids made it to the Chunin Exams, meaning a minimum of 8-9 missions. Remember Iruka tested Team 7 before the exam to see if they were ready. Thinking or hoping someone tested the other teams too. Which means those sensei had to put in time with them.
As for drill sergeant Kakashi, not sure if you’ve ever taken martial arts, but I have/do. Sensei are not the nicest people by any means- out of the dojo, they can be, but on the mat, when training, you might as well have a drill sergeant. They yell in your face, they throw you around (painfully). They want you to be serious and understand the seriousness of it. They are training you to fight and yes, you do learn techniques that can be lethal and how to use weapons irl. So, they have to be serious and they do work with you based on your own skillset. So, there’s some merit to that, historically. So, in a world that’s built around the shinobi system, Kakashi as a drill sergeant-sensei is possible and that doesn’t make him any more/less good or bad than the other sensei. Same for Kakashi as mentor-sensei. I think he became Team Leader Kakashi with the introduction of Team Kakashi, when he acknowledged them as his equal. But at the end of the day, why can’t he be all three? There’s a time and place for each role and no one size fits all approach to teaching. At the end of the day he was trying his best. They all were. And he was a good, but flawed, sensei. They all were.