Hmmm, last I checked hero0 had some inaccessible screens that you couldn't get passed, I don't know if that is still the case however.
There did also used to be  super hero game in the storm8 series like zombies live but I think that's gone down along with their others.

one game I've heard about but never tried is mind sight which is I believe an interactive audio adventure where you play a blind superhero for ios, here is the applevis entry, that is actually one I need to investigate further myself.

There are also plenty of standard zcode parser type of interactive fiction games kicking around with a superhero theme, going right back to Scot adams Hulk.
of that series I personally can the earth and sky trilogy by Paul panks. The first two are available in zcode, the last is a glulks game, but a quick search on the if encyclopedia should turn them up.
They even have a great help system and a cool ongoing story, about a brother and sister who's scientist parents go missing leaving them with two super powered suits, one with super strength the other with flight, fog and electric powers.

There also used to be futureboy, an interactive fiction  game about a super hero in a future city which had sound and music, despite the fact that it was a full parser interactive fiction game, though sadly i think it's no longer available.

Lastly, there are actually several of the choiceofgames and hosted games titles with a super hero theme, such as community colidge hero and heroes inc, though I will second Aaron's recommendations of the hero's rise series, ---- and from someone who does't generally regard super heroes as a favourite genre .