@BanditHadron
For the very reasons I've already mentioned, but if needed to make it even simpler:
The more important a detail, the more it's referred to (even in just small hints) in a story.
Princess being the original successor - multiple times.
Royal family having this as a duty - 2 or 3 times.
Only females assume this role - once.
From that, so far the fact that it's a female only role doesn't seem important or at least not as important than it being being a member of the royal family. If one character would have at least said "As the princess of this kingdom you were chosen" or "As a female of the royal family" it would have make that fact stand strongly but that's not what happens. Even in her monologue the princess focuses on the fact that she has high magical power being her reason for being chosen...not that she was a female of the royal family. You got to realize that even the most subtle of dialog can assert the importance or lack of importance to any given information.