Of course, once you've done that, you do have to vary them somehow. If you have vampires and/or werewolves among us, it's urban fantasy, even though you can easily put both in a superhero universe. If you have genetically engineered supersoldiers in power armor or even a flotilla of infant alien refugees who look human but have powers and abilities far beyond those of mortal men, you are writing science fiction.
How random varies a lot. One novel has everything triggered by some kind of unexplained artifact which granted varied powers. On the other hand, one had an Event, after which about one in a thousand people in traumatic circumstances develops a spontaneous and useful power, based on the trauma and the personality -- that can work from everything from "vampire" to "mad scientist whose gadgets don't work when anyone else build 'em" to even weirder things.
But in both cases, the meta-origin influences a lot. For instance, since traumatic circumstances are much more likely in public, that was a universe where secret identities were rare indeed. A world in which superheroes found artifacts in odd corners would make it much more likely.