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So this began with a discussion in the Laconic Description Improvement, and ended up in confusion as to what this trope is actually about.
There seems to be two conflicting ideas written on the description: one is that the princess's royal lineage and upbringing is a plot relevant aspect of the character, the other is that the princess's title is completely irrelevant, but it's just tacked-on to the character to add her "specialness".
In practice, it seems to be used as "Princesses exist".
As you can see, the trope is mostly used as a pothole magnet. And many of the ones that give "context" to the example doesn't actually touch on the character's royal status and makes irrelevant tangents about their other traits instead.
There are some examples that at least attempt to give some sort of definition to the trope, but they're really few and far in between, and most of them are covered by other tropes anyway.
I don't really see anything worth salvaging from this "trope" so the only proposition I can think of (outside of outright cutting it) is to turn it into a redirect to Royalty and Nobility Tropes, since this is basically an index for Princesses tropes.
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How well does it match the trope?