The whole idea about any superhero media is a special dude going on a violent spree because the authorities (in their eyes) can't do their job properly. The whole concept is anti-government and society as a whole.

Not at all. They have their roots in the projection of a defined moral trajectory that the superhero is charged to lift society along and the disagreement they have with the state is that it can't do that enough, not that it's going in the wrong direction. Modern superhero stories have completely inverted and fucked with and abandoned this narrative but the original stories were absolutely supportive of the state, fundamentally modernist.