Is being a bad person so irreconcilable with being not being an evil person?
No, but I don't think it's a tall order to ask the story treat said character that way. Unless of course it's a straight comedy or the entire cast consist of assholes. Plenty of series have pulled it off well. This one doesn't, which is a shame because it pulls off every other supporting character.
And Vegeta really isn't the same. The guy started off as a villain and was a major threat for an entire arc. Sure, it's a bit weird people forgave him so easily after that (something I honestly did have a bit of a problem with), but DB/Z isn't a school setting and his alliance with the main cast was more based on the fact he was needed and not that they thought he was a good person until much later when he had completely turned over a new leaf. And even then, the guy still goes to hell when he dies.
Edit: And honestly, how Vegeta is treated by the story is kind of shit too. Almost every conflict in Z is indirectly and directly a result of his douchebaggery and need to fight strong people.
The thing that makes it different is Goku isn't much better and there really isn't as big of a gap in character writing quality in DBZ as there in in MHA. Everyone is kind of shitty in different ways.