The problem with being too inclusive is that you allow in examples that display none of the virtues of the category in question.

To my mind, science fiction is good because it provokes thought; it encourages critical thinking; it produces genuinely valuable speculation; it has a quality of cognitive estrangement and defamiliarisation (where, for example, you suddenly find your ordinary life to be quite startlingly strange); it teaches you science (or better still, makes you want to learn more science); it brings the past, the future, and distant worlds to life; and probably quite a few other things I haven't thought of.

Furthermore, I think SF should deal with the possibilities implied by the premise. If a woman discovers she can levitate, then gets involved in a lengthy series of events that have nothing whatsoever to do with her ability to levitate, one may wonder why the story wasn't about an ordinary woman.

I do not consider superhero stories to be SF, regardless of the rationale behind their superpowers. Let's face it, the existence of djinn or Greek gods randomly bestowing powers on heroes is better science than the idea of genetic mutation giving somebody metal blades in his hands. All superhero stories are fantasy, then, but then, all fiction is fantasy, and we tend to have certain expectations of things labelled fantasy. So it would make more sense simply to call them Superhero Stories.

Superhero Stories are of little interest to me, partly because they tend to have none of the virtues of SF that I listed above, and partly because it's bloomin' boring to watch people punching each other through walls and doing generally impossible things that I can't relate to, then angsting on about it.