It's like the anime/manga but everyone's quirkless! Which means a few things changed if you truly think about it.

1) Momo is rich but in a different way. I'm just going to say that pro hero's are just popular business people so Momo is born from popular business people

2) Midoriya and Bakugo are friends. Bakugo bullies him because he was quirkless but with no quirks there would be no reason to bully him. But if you want him to be cocky and rude still and bully Midoriya we can just say that he was praised for immense success in schooling and a child and Midoriya wasn't, making him bully him for him being dumber than him

3) The todoroki family. Okay, let's get this straight. The whole reason of todoroki being a sad child is because if quirks. His father married his mother because she had a powerful quirk. But for this we can just say that Endeavor owned an incredible business and needed a child to continue it. He married a women even though he didn't love her and had four children. The first three didn't have the best personality for the job so when Shoto was born he molded him to have the correct personality. Out of rebellion Shoto dyed his hair white and red. His FATHER was so pissed that he forced the mother to spill the burning water on his head face

4) UA is a business school. No quirks=No hero's=No need for hero training. Due to this you and everyone else are in a school to learn how to be successful in business or it could just be a really good high school, your choice!