I agree some of the other commenters, your perspective is that women are just better than men. According to you, they're kinder, less violent, more inclusive...etc. I think Carlyn made a compelling argument that women and men are not that different in this regard. I would rather a world where men and women worked together instead of replacing the patriarchy with a matriarchy.
Your statement:
But if we hypothetically ran the show from top to bottom, the level of violence and war would likely decline significantly because we would then be matriarchs, not patriarchs in skirts.
In this hypothetical world, men would have no power and women, running the show from top to bottom, would have ALL the power. I'm not sure what that means to you, but no power sounds like slavery.
So it sounds like you're saying that we can only achieve peace if men become slaves to women. Is that right?