Can illegitimatize. Not necessarily. It's not exactly difficult to have the conflict and the drama hinge on other things.
Certainly I wouldn't call what you're talking about to be a significant point vis a vis the anime in question -- near as I can recall those were only disabilities and sacrifices occasionally, and were mostly just somewhat edgy excuses for superpowers :V
Which should be okay. You can still have a nice story with all the bells and whistles with barely acknowledged edgy superpowers. Sometimes it's fine if parts of the backstory et al are just kinda' there.
... doing it the other way is also be about the quickest way to get me to stop watching something, though, heh. For me, hammering the nail that the world is terrible and success only comes through suffering for the Nth hundredth time cheapens any emotion they were trying to draw out, just as well. When I want shitty messages of that sort alongside the rest of the narrative I go watch the news or read the classics.* It's nice to see folks shucking those influences, to whatever degree, y'know? Doesn't cheapen the emotions involved, it just emphasizes other ones. Which is often quite nice. I like those emotions better, and human brains being what they are we really do need more of them in our lives to offset the inclination towards negative one, imo.
*I rarely watch the news and you would probably have to shoot me to get me to go back to reading classical literature, and probably shortly thereafter have to stop me from shooting myself.