That's probably what I would do. Superhero-style games are pretty easy to run that way. No need for some big organization giving orders or a major plot overall, but there are various plot threads people can follow in the form of recurring villains or the like. And in general, if things need to be shaken up, a villain can appear and do something.
Sandbox stuff also works well if people can play heroes or villains themselves, and thus provide additional things to do. As far as setting goes, there's probably the question of scale. It could be some sort of "emergent heroes" sort of game where super-powered anything is just starting out, and thus characters are presumably not super-strong but expected to grow, or it could start with more things established (say, early Justice League) where people are stronger but the threats are bigger and it's less "your city" than looking after things across the globe. I don't think I'd start things at the level of galaxy-spanning adventures, but they could always get there.
As far as a general setting goes (prevalence of super powers and average "power level" aside), I could make something from scratch, or I might give another crack at using the one from Double Cross, which establishes a lot of things (including all superhumans sharing a common origin).
