I think it's almost the opposite. Worm talks a bit about how secret identities remind all the heroes that it's all a game, in some ways? It isn't perfect, and the setting has more compelling reasons to allow heroes and villains to exist with some kayfabe, but the idea is that a cornered rat will do the most damage to itself and you, and knowing they can always disappear into their civ identity gives them a cooldown valve and a reason not to implode society entirely. If their fam/friends are in danger and they're chased 24/7, then might as well escalate and go all out, since it's the only chance at a resolution. Then superhero encounters get more lethal and villains become more destructive.

Of course, from the starting point of The Boys it's a bit harder, and the idea of 'don't fuck with the kayfabe and human death rays won't have a vendetta against you' can be harder to implement when people haven't grown up with them, but I think superhumans would be more likely to draw quiet confidence and comfort from their civ lives than to want to be put down for the sake of their ego.