With Bakugo, though he was giant asshole in the beginning, he does learn from serious lessons. He was a big fish in a small pond during middle school but when he gets to UA, he then realizes that he is NOT the most powerful, nor is he the smartest. Not only that, but he also realized that while he never thought about improving himself nor studied his opponents, Izuku studied HIM. Izuku, who has been bullied by Ka-chan, had spent a lot of his time improving himself to the point where he bested Bakugo not just by knowing his moves but also to complete the test.
Bakugo ends up being greatly humbled (despite not acting like it) by all of these revelations. He isn't hot shit. He ends up being seen as loud annoyance by a lot of his classmates because of the same attitude you described. The only guy who manages to get close to him, Kirishima, is well...a really nice guy who admires Bakugo's "I don't give a shit" attitude.
I think for a mean character like Bakugo to be liked, there has to be a lot of humbling going on and then actual development. Bakugo doesn't stay the bully. He remains loud, and bombastic however no longer does he look down on everybody. He actually matures enough to get REAL goals and work at those goals. He see's Izuku and Todoroki as worth rivals, and does treasure the friendship he has with Kirishima. He doesn't take it easy on Ochaca because he doesn't want to cheapen the battle against her AND he doesn't underestimate her. So we have a previously loud, aggressive bully eat a lot of humble pie and then show development.
Kinda like Vegeta, ANOTHER mean character who was a complete DICK when he first appeared, then after repeatedly getting his ass kicked, realized that maybe he ISN'T hot shit and needs to ACTUALLY grow as a person. Umi, from Magic Knight Rayearth, was a spoiled rich bitch...who got humbled by being put in a terrifying life and death situation and managing to rise to the occasion. Kyoko planned on KILLING Sayaka and Homura to get all the juicy Grief Seeds, then get's humbled by discovering the truth about being a Magical Girl.
It's that humbled aspect that helps the character gain traction. A good dose of eating crow really helps make a mean character likable...as long as they show an evolution. They can still remain abrasive, but there is an acknowledgment of their shortcoming that helps them grow.
Now...why is a character like Mineta STILL ALIVE!!?! I HATE THAT LITTLE PERVY SHITSTAIN!