Superheroes commit acts of war, but are trying to "uphold" the local formalism, not change it.
Superheroes are parasites.
Basically: Batman should conquer Gotham. If he runs the place he could simply fire every corrupt cop, then hire sheriffs to suppress crime. Maybe even train them himself.
Gotham has a problem because Batman refuses to conquer it.
Why does Batman refuse to conquer it? He doesn't want to be held responsible for what Gotham is or what it does. He just wants to play around in his playground, like a degenerate fop. He gets his jollies from punching folk; if he cleaned up the streets, who would be left to punch? He would have to stop. Can't have that.
Indeed should someone else - Superman maybe - try to conquer Gotham so as to re-enable crime suppression, Batman would actively oppose them. He acts like he owns the place if and only if you're trying to own the place honourably and up front.
You can see this with "saviours" in real life too. If you do anything that addresses the root cause they drop everything and attack you ferociously until you're defeated or they die. Effective Altruism as in Effectively defending the problem they want to be ""altruistic"" about. E.g. a lot of doctors will resist healthy anti-pyramid diets, should you be foolish enough to ask them about it. This isn't because they're brainwashed; this is precisely because they know their bread is buttered by pills and surgeries, not by healthy non-patients.