You can be wrong. I'm okay with that.
Why can't a hero have negative qualities?
Why can't Bakugo just be a troubled youth with anger/insecurity issues, are you saying such people don't exist, you don't think there's a huge gap between school bully and person who ostracizes themselves from society by breaking the law and actively wants to murder/ruin people's lives?
Bakugo isn't Satan/a sociopath.
Why isn't he in jail for exploding people or something?
Because Bakugo doesn't go around exploding people, he's literally asked by his friends in episode one if he wants to go with them to the arcade and bully some people and Bakugo responds to them by yelling about how he won't do that because it would go on his record and ruin his chances at becoming a hero/getting into Yuei, Bakugou is serious about his goals.
Like seriously, what does "he's supposed to be this star pupil, but..." mean?
How does Bakugos image in any way whatsoever conflict with his intelligence/skill?
Hell, the route you're suggesting for Bakugos character doesn't even allow him to interact with Deku whatsoever so how can you say that would have been a better place for him?
Might as well write him out of the story completely.
"Bakugo could be a great character if he was this violent crazy anti-authority, anti-society villain who just wanted to tear shit up that Deku encounters and he's this villainous rival."
Putting a hollow ideology being him and making Bakugou into a more generic character would make him better how?
I find it much better that Yuei is taking an active role in making sure Bakugou is shaped into a proper hero rather than just throwing him to the wolves, it's more than realistic that in a society such as this people like Bakugou would slip through the cracks now and then.
(and if you're wondering what Deku or some fans of the series find admirable about Bakugou it's his drive/passion/strength, for me it's enough to offset his more negative qualities, not that those negative qualities don't make him entertaining as well)