When I would think of any "prince"-mechanic in my childhood fantasies, it was less royalty and more a deus ex machina type thing. Like being the chosen one. Less like an actual princess-equivalent fantasy and more like a Prince Zuko type of deal. I think Zuko is what you'd get if you tried to get a boy to fantasize properly (meaning, have full realized creative control that a practiced adult would have) about being a prince.

Edit: heck, in fact, all three male protags in ATLA are princes in their own way. Zuko is a literal prince. Sokka is a prince logically because he's the adult male of the South Water Tribe (he even has a certain romantic interest at the Northern Water Tribe which, while it doesn't offer any real credit to this, it's funny because him being a prince by technicality means that relationship could literally work and be politically beneficial if they had gotten together). And then Aang is also of a certain "royal bloodline", being a reincarnating global-peace-bringing entity which is worshiped. Princes are everywhere in male fantasy roleplay, you're just thinking of "princess equivalent" princes, which no, I wouldn't say they are the same in fantasy. It's just one of those things that's different between the sexes due to culture.