I agree that both sets of characters, princesses and superheroes, should be restricted, because of the marketing to children element, but I think the "problem solving" justification is silly. I would ask:
What constitutes good problem solving? What is an example of a children's character who exhibits good problem solving? For every specific individual character being banned, what, exactly, specifically to that character, is wrong with that particular character's problem solving?
I have no problem with princess or superhero stories
. We love some of the original "princess" fairy tales, which were originally morality tales. The much-maligned Cinderella, for instance, is in the original story being rewarded for her good heart, in contrast to her vain, superficial stepfamily. But the Disnified Cinderella is part of the marketing scheme promoting vain, superficial behavior. Disney and Barbie and pop culture have corrupted these stories about honor and sacrifice and duty and morphed them into the snotty/bitchy/sexy/arrogant/snide/bossy/vain/materialistic/"girl-power" divas we all know and hate. We've had several conversations at our house about real princesses and civic duty and sacrifice. The same is true, I'm sure, of superheroes, although that would be my husband's area of expertise (he's interested in classic comics). But I know that many of the comics are more complex and sophisticated than the bang-bang-pow-pow-shoot-the-badguys stuff that's peddled.
Preschool is a bit young, but if I were teaching older kids, maybe middle school, I think it would be great to do a "fairy tales and comic-book heroes" unit in which we examined the stories, their messages, and how they changed with marketing.
ETA: I think it's funny that so many object to the princesses' being passive. That's the least of my objections to them. I'm all for passivity.
But, vanity, selfishness, materialism, and shallow power-hungry greed, not so much.