@lolipedofin Yeah, it has been a problem from the beginning that there seems to be nothing concrete holding up the women's superiority in the society. It's purely cultural, also structural to a certain degree but by far not thoroughly. Angie's old man clearly had real political power and responsibilities. Between Angie and the prince, it looked all the time like the prince was the more important one. The queen seemed secondary to the king. I'm not sure if that's haphazard inconsistency in writing or what, but it does erode the general atmosphere of the female privilege. It's possible in the distant past some terrible war killed most of the men, leaving the women to handle all administration, creating the roots of this supposed situation, but it would clearly be a long time ago and there's nothing explaining why the effect would still linger so strongly.
All in all, the real reason must be the otome game background. Games often have a forced setting for no other reason but to make the game plot work. Some games would go the extra mile to explain why and how, but I wouldn't expect a dating sim to bother with it.