I hear what you are saying, but this approach puts the burden on the woman to leave her job and make the change. The victim shouldn't have to accommodate sexist policies. If you were a man, would you quit in solidarity to help send a message? Doubtful.

There is always rivalry. The problem for women is they bring it out more in men with ego problems.

There's a lot of rivalry amongst women too, it just plays out in different ways and different domains. You can even see this in OP's distrust of the "soft skills" 'team' - that part of the enterprise is precisely where rivalry tends to matter the most.