I'd guess it's because queen = mom to a little kid. The princess is young and has a mom and a dad, much like yourself at that point, so she's more relatable.

I was an UNSTOPPABLE princess. I had pink hair and a pet dragon and shapeshifter magic and unlimited extra lives, and was always saving everyone from evil wizards or Shredder or Bowser or Ursula the Sea Witch. As usual, all my games blended together, so there was no real distinction between playing Princesses and playing, say, Gold Power Ranger Princess From Neptune Braves The Temple Of Lava To Find The Magic Diamond That Will Lift The Turned-To-Stone Curse On Her Friends.

... Shit, that STILL sounds awesome. Somebody get Michael Bay on that.