See... Maybe this is a preference of story scope and power levels but...
I think Superman or the Fantastic Four could.
We're talking about a universe in which some individuals or groups of individuals have more resources than individuals, than nations, than -- quite frankly -- our entire real world has put together.
People who can create black holes and escape their impossible pull in the course of an afternoon. People who can find, locate and acquire every ounce of gold of earth, make diamonds in their hands, observe and process the electrons orbiting around atoms. People who can know and recognize a person based on their DNA. People who are prepared against nuclear attack, who can travel between and create parallel dimensions, alter probability, walk through people's minds on a friendly stroll, rebuild shattered worlds, hear a heartbeat lapse farther than the speed of sound can carry it, sense danger a day away, wrestle angels, thwart gods and challenge rogue universes.
A world with superheroes a land where the blind see best, the children never grow up, the mild-mannered deflect bullets, the wronged avenge, the warriors make peace, the peaceful aren't forced to compromise and milk and honey are practically produced on tap by molecular replicators.
That isn't to say that superheroes don't have their share of problems but the twisted, bitter comedy of it all is that their problems, in spite of the remarkable feats they attain, are our problems. Medical bills they can't pay, women that won't give them the time of day, cheating boyfriends, overprotective parents, diapers that need changed, obnoxious bosses, impossible deadlines, dry-cleaning bills, unexpected expenses, government regulations, annoying co-workers, broken down transportation, death and taxes.
But they still recover from all of these things... These ills just give us a basis to relate, a moment to connect with. Eventually, the hero escapes just long enough for us to breathe a sigh of relief, enjoying our cartharsis, and then is promptly plunged back into the wellspring of the imagination to see how far they can be submerged into the collective unconscious notion of "adventure" without drowning. The key is that the heroes come up for air when the readers do. If they do so before, readers get bored. If they do so late, readers turn elsewhere for cartharsis and abandon the character to drown alone.
But "reality" and "relevance" where super-heroes are concerned is a game of chicken between creators and readers.
It's playing poker -- only the creators are the house and it's their job to win.
If it is a game of counting cards then with the right story and well-chosen words, a writer can accomplish anything. It may take a few hands... But I don't think it's outside the realm of possibility for super-heroes to score the ultimate happy ending and make a total break with reality.
However, I think the trick is that readers are trained to ask, "What next...?" and the writer needs to be six steps ahead by the time someone thinks to ask...