Responses
Royal families often had a lot of inbreeding issues, because they wanted to keep their bloodlines pure, so some fresh blood from a commoner woks wonders.
Combine that with the upbringing in an environment that makes you believe you are something special because of your bloodline, and you can see the outcome.
Meanwhile, the half blood princes had to live in the real world, so she needed common sense.

No seriously, all the royal pure bloods in this family have issues. Meanwhile, it’s only the little halfling princess, born of a commoner, who managed to inherit common sense.