Since the author is pinning one star reviews, here's mine.
The premise of someone normal training only his body and combat techniques in a world with super powers is fine, many heroes without any kind of super constitutions in the original work can tank hits that would turn any normal human into chunky salsa. Aizawa for example can jump 3 meters in the air, get hit by some guy with hulk tier strenght and NOT become fine red mist on contact and is basically an anime ninja in all but name.
Add to that the absurd science fiction technology of the show, there really isn't much of a reason why some "normal" guy in that world without a quirk couldn't become a hero if he puts the effort in it besides the "It would make other heroes look bad in comparison" reason, but that's besides the point, the point is that the premise could totally work.
The reason it doesn't work is becouse the MC is both a nice optimistic guy that's very likeable and also rabid dog hellbent on destruction, and the longer it goes the less excuses you can make for the former because of the latter. There's absolutely no reason why he, a person that probably has a body count in the 4 digits by now, should be outside a psychiatric ward, or just jail, specially in a world where everyone is obsessed with morality, law and justice. The reason he gets away with it for most of the novel is becouse... they like him better? At some point it starts to read like excuses you would hear from “Pit Mommies” after their pitbulls start mauling mailmen and eating babies, here's a dramatic interpretation of the first 100 chapters
Some Hero: "BULLET, STOP EATING THOSE VILLAINS RIGHT THIS INSTANT!"
Bullet: *Sad Puppy Eyes*
Some Hero: "Awww, i can't get mad at you, but don't do it again, okay?"
Bullet: * Does it again for another 100 chapters*
Later on he gets WORSE, his multiple personallities merge and he starts speaking in what i can only describe as "Cocaine Addict Speak", he can not stop talking IN ALL CAPS about murder and violence and how much he HATES society, the hero system, villains, his lot in life. Everyone that likes him just, kind of, ignores it, even if the only topic of conversation he can muster now is murder. Everyone that dislikes him is just there to get humiliated and to point out that he's quirkless and therefore less than human.
That's another thing, i don't think there ever was any kind of discrimination against quirkless except for Hero related jobs, quirks are basically irrelevant for most of society becouse its ILLEGAL to use them without a hero licence outside some very mundane activities, some people even lost their quirks and it was seen as a tragedy, being quirkless is a very "Unfortunate" event, its pittable, its the same as being a cripple or having some other disability, it would be like saying society today has this huge grudge against people in wheelchairs or people with Down's Syndrome, its just nonsense, even the people that feel unconfortable around them would still fake smile to pretend to be civil, even more so in a society that worships super heroes.
Those are the 2 main points why it doesn't work, characters personalities twist and bend to acomodate this MC that can not stop killing people.
