By definition though, that would not be specifically a Patriarchy, which gives power to men via sexism.
It would be an Egalitarian hierarchy where anyone competent could and would ascend, be rewarded, and everyone has a chance to be valued.
That's the goal of feminism. To replace Patriarchal dominance hierarchy with Egalitarian hierarchy fostered in a higher emohasis on collaboration and a reduction in overkill competition (but not competition entirely).