Beg to differ... Deadpool, Blade, any of the noir type supers, both in the 30's/40's and the 90's/00's...
Deadpool fights evil because it amuses him to do so.
Blade is a hero in the greek sense - the protagonist and one the audience is supposed to emotionally bond to, and has superpowers, albeit from a supernatural curse...
Ant Man is, well, pretty much mercenary at first. It's a Job.
And then there's the DC Television Multiverse, most specifically Batman and both Arrows... Ollie at first is fixated on undoing the corrupt legacy, no matter whether or not the side effects hurt those nearby; only later does he start to take into account the side effects other than being caught. Thea, once she dons the hood, wait, no, from the get-go, is fixated upon personal goals that just happen to include taking down mostly the same folk as her brother, and getting totally blotto drunk and/or stoned. Then we get both Black Canary and White Canary... both radical serial murderers... just ones who take on individuals who happen to have gotten away with things. Oh, and Flash's mentor is a time travelling universe hopping psychopath... The only ones that really are specifically
The Arrowverse is divided; we have the Arrow series with a bunch of wealthy sociopathic putative heroes who happen to do less harm than good, and Batman, who's no better, vs the genuinely out for the common good Flash. I didn't see enough of Constantine to know much about him.
And that's before the local hero who is just ideologically opposed to other supers... Baron Dr. Victor von Doom...
Not always presented as a villain. Not always presented as a hero. Really doesn't give a rat's arse about anywhere but Latveria and, for sentimental reasons, Marvel's version of NYC....
And, of course, there is The Hulk. In his Bruce Banner phase, yes, he cares. When in Hulk Mode, he's more a force of nature than a heroic being... but usually, when hulked out, either Bruce aimed himself at the bad guys or some other hero directs him... at least until Bruce learns to... "Stay Angry."