There do exist at least a few superheroes who are trying to change the status quo proactively. I don't actually read that many comics, so I could be missing quite a few instances, but here are some examples:

• Tony Stark a.k.a. Iron Man (movies): stops developing weapons and begins developing Arc Reactors instead, in order to eventually supply the world with limitless free power.
• Tony Stark a.k.a. Iron Man (Civil War comic arc): dedicates a lot of effort to the Superhero Registration Act, in order to make superheroes accountable for their actions. Is ultimately proven wrong, I guess.
• Professor X: wants to make the world a more tolerant place through a combination of charitable donations, public outreach, and, when absolutely unavoidable, mind control. Contrast his approach with that of Magneto, who wants to accomplish essentially the same thing through conquest.
• Reed Richards: pretty similar to Iron Man, in that he is slowly trying to uplift the rest of humanity to his own super-technological levels. Creates the whole Negative Zone fiasco when he decides to think like a supervillain during the Civil War arc.
• The Flash (cartoon, some comics): When he's not facing the existential threat of the week, spends his time on infrastructure improvement projects, community outreach, education, and other such activities that many other superheroes feel are beneath them.
• Daenerys Targaryen (books): Though initially motivated solely by revenge and personal survival, she stops long enough to overturn several existing social orders in order to improve the average quality of life. An arguable example, since no one in ASoIaF is particularly heroic.

These examples are just off the top of my head; I'm sure there are others.