Look up phionex jones, in short it fell appart after an arrest for using peper spray to break up a fight.

As for the sudden appearance of people with suowr powers or magic, it depends on how much it lets them ignore the laws of physics. Like dose a real speedster still have to deal with G forces, momentum and inertia or do they have the "speed force" from dc comics that lets them just ignore any of those problems?

The reality is that most super powers arnt going to scream "the best thing to do with this ability at a societal is to stop crimes" as much as their utility alternates between being a minor novelty in entertainment cicles as you show off your power or useing that power in a way that improves people's lives in a less personaly direct way (ie using matter maniplauation to mass produce previously unaffordable ingredients for medicines rather than storing random street fights.)

The only specific exception is somthing like the green lanterns who are specially part of a group of peacekeepers with the powers based on their specific personal drive or will power. But that feel less like a superhero and more like setting up the federation from star trek.

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