But All Might, the most popular and possibly most powerful hero in their world, shares our definition of being a hero. That shows how the concept of being a hero is also idealized in their universe. Maybe most people forgot it after so many heroes kept popping up, but self-sacrifice and classic heroism was definitely the foundation of the hero occupation. Heck, All Might became popular precisely because of his heroics in saving people.
Going back to what I said (the line you quoted), I did include the word "ideally." I do agree it's possible for assholes to become heroes in their system. But they shouldn't. A bully like Kacchan doesn't deserve the power and fame he'll get when he graduates and gets a license. He'll probably abuse the hell out of it, like how those asshat heroes in OPM picked on newbs or pushed civilians around.