I've been thinking bout the world All Smite exists in would look like 🤔
Enij Todoroki would still be a bad father if All Might was All Smite.... Dare I say, even worse.
Ok so Endeavor's whole thing about his abusive behavior was that he wanted to surpass all might, and so he "trained" both Toyia and Shoto right? If All Smite existed then Endeavor would have an even bigger obstacle + he'd probably get the idea in his head that "it's for the greater good" as a way for him to justify the torment he's putting his children through.
Enji Todoroki as the #1 would likely realize that he can't beat it even restrain All Smite on his own. So what does he do? Not only would he get Natsuo and Fuyumi in on the training, Toyia would have never would have gone into those woods.... If his father is giving equal amounts of "attention" to all of his kids Toyia wouldn't have had to prove himself. After all, 4 children to fight beside would dramatically up his odds of success. Not only that but 4 hero children would likely be a boost in the public eye/ a beginning of generations of heros like the Iida family.
Oh but don't be disappointed Dabi lovers, I think by the time Shoto is ready for UA, Toyia would have already faked his death. He likely wouldn't become the Dabi you know, more focused on getting his siblings out of the abuse than revenge. Toyia also would have a strong bond with Shoto because they both showed the most "promise". On the topic of UA, I think that Midoriya would still attend, with OFA.
Let me explain, in my mind All Smite is a hyper violent vigilante/ Stain if he did an extensive amount of research on his victims/ protector of civilians (I'll explain more later). All Smite is a good guy deep down, and supports Midoriya's dream of becoming a hero with all his heart. Dad Smite basically. Also I think that anyone inspired by All might (excluding Izuku) in canon follows all smites path of "Villainy" ex: Sir Nighteye, Cathleen Bate/ Star and Stripe.
Midoriya eventually confesses to his friends about the good that All Smite does from the shadows
taking down trigger distributers
controlling illegal weapons
defending citizens
squashing any dangerous organizations
helping the quirkless
helping abused and orphaned children find good homes
everything the Hero Public Safety Commission doesn't do
Good things that All might can't do while being restricted by the HPSC
So that covers a lot, so I'll quickly run through a couple of characters that would be changed by these things and why
Keigo Takami- would have been saved by All Smite when he was 6-7 instead of Endeavor. All Smite being a villain would have known about how abusive Keigo's father was sooner than Endeavor
Tomura Shigaraki- would have been found by one of All Smites underlings before AFO
Twice - actually becomes one of All smites underlings shortly after his trauma
Dabi- dabi went out looking for smite to fight, ended up joining him
Himiko Toga- found dirty and alone by Sir and was brought in
Eri- Sir and Smite raid the Shie Hassaikai slightly sooner than canon, right as the bullets were being produced. Smite originally did it to crack down on the bullets, but then saved Eri (with Izuku's help) and found her a home with Eraserhead
Shinsou- poor baby was abused in foster care for his Villainous quirk, his latest foster parents decided to try and sell him off, but luckily Smite got a hold of him. Shinsou is going to UA with Midoriya and lives with Eri and Eraserhead.
Present Mic - Mic, Eraserhead, Sir Nighteye, and Nezu all secretly work with Smite to keep Japan's underworld from becoming it's over world. Present Mic is only slightly different from canon, only now does he have an old scar on his lip from being muzzled from when he was in the foster system.
Eraserhead- the same as canon and as mentioned above, but his scar from the Nomu fight doesn't exist, but instead it's on his eyelid from a knife fight against a villain on trigger.
Hmm what else, oh yeah!
Midoriya and Shoto are secretly vigilantes and work with all Smite, Natsouo and Fuyumi are both badass ice heros, while Fuyumi still tries to keep peace, the men in the house are constantly at odds. Rey isn't in a hospital, but presumed dead. ( She's not shes has been rescued by Smite, it was Shoto's idea)