Why don't we have more Disney prince stories?

I would venture to guess that it's due to marketing. Being a princess is a very common fantasy among young girls that probably predates the Disney Princesses franchise. The combination of romance and beautiful dresses has a big appeal to that demographic.

On the flip side we have the male counterpart: the prince. For the young girl demographic the prince's appeal is as the princess's consort. An important part of the story, but not the main focus. Now we go to the other demographic, young boys. For the most part what young boys want in a male lead (basically what they want to become when they grow up) is a dashing warrior figure. The accompaniment of things like royal heritage and dress isn't as important as the sense of adventure and rebelliousness he brings. So a male lead being a prince is not important. As you've noted in the examples you've supplied most of them are only superficially royal.

There's also the (perceived) boy-only stigma that the term "princess" brings. The Rapunzel movie was renamed "Tangled" without any reference to her being a princess in an effort to attract the young boy demographic. I suspect it's the same reason why the US trailer (and other marketing material) for Frozen put less emphasis on the royal sisters and gives more time to male characters such as Olaf.

So for pure marketing purposes movies with a female lead get spinned as princess stories, and stories with a male lead tend not to do that.