The answer is simple. It's men's fault (as is the case for so many things).
They liked batman when they were kids, cuz heroes are kids things, but as soon as they grown up and those thing they like are being criticized they cant handle it and isntead of saying “yes, its childish and silly but I like it” they deflect and say “Its not childish at all! Look its bloody and gore!”
Men are cowards and cant even stand up for the thing they love
This is part of socially conditioning the rest of the world to accept male abuse.
The “anti-hero” became a played out common staple rather than a rule-breaking trope around the same time a cultural shift occurred away from traditional values and keeping up appearances with old norms. Honoring the tortured-hero-with-questionable-methods (as well as the society-made-me-homicidal villain) is directly in line with men’s recent, largely successful, attempt to reframe abusive behavior as the uncontrollable product of some deep hidden pain - so feel sorry for them, right? And think how noble they must be for not being worse.
Men are latching on these dark, damaged characters because they want to see themselves and be seen the same way; all their worst parts inevitable, understandable, and, of course, “cool.”