ittsme
All your logic doesn’t necessarily support your conclusion
Your conclusion is a rather feministic theory and as a general rule I think we can be dan lkav zchus that chassidush rabbunim have more morality than what you are suggesting.
So whats the answer
First you need to understand that the answer may simply be, its tradition.
I am a litvak, and therefore all your questions are questions that I would ask.
But thats not how chassidum look at things. I have chassidush relatives and they look at anything that is traditional as halacha. They don’t ask questions (not halachic nor modern ) on an established tradition.
Even though that’s not how I do things, I respect that approach to our religion.