"We're getting sick of these damn romance movies between a prince/princess (or someone of high-class) and a commoner/non-royalty."
Not that I'm agreeing, but that's probably a more specific statement than "princess movies" which might be mistaken for a film that features just a princess.
Cinderella
Sleeping Beauty
Lady and the Tramp
The Aristocats
The Little Mermaid
Beauty and the Beast
Aladdin
Hercules
The Princess and the Frog
There were a lot of films I didn't know if they fell under this category though, like:
Snow White (A prince arrives, but it's at the very end and not the main focus)
Tarzan
Mulan
The Hunchback of Notre Dame
Pocahontas
So maybe it's to an extent, we're sick of "romance movies", which even Lion King has, but it's weird, because Disney didn't make as many romance films in the 2000's and they didn't do as well [compared to the 90's films] (Atlantis, Home on the Range, The Wild, Bolt. They did have a few successes like Brother Bear [I think?] and Lilo & Stitch.)