This is a perfect example of being both over and under qualified for the same position.
Prince has the job, has the authority, and practically everything in the bag, but it is his sister that has the higher charisma stat, so she just attracts people's attention all the time. She would likely make for a decent leader too, but just does not want to do it.
The prince is perfectly fine for the role, but is nothing special. So he gets overlooked and/or judged by the same filter as his sister. And that his sister is a gold ranked adventurer does not help his case at all. Kind of interesting as you do not see a person be both qualified and unqualified at the same time too often.