I don't just mean women in charge, for example when Margaret Thatcher was PM that wasn't a matriarchy - she upheld typical patriarchal systems. I mean in a world primarily shaped by women - some examples might be medical research using female bodies, women seen as the default human.
Would we fall into the inverse problems the patriarchy presents? i.e. the patriarchy can hurt men as well as women - they can't express emotions other than anger because that would be gay or feminine. I wonder if motherhood would be put on a pedestal (though patriarchy has done this forever without actually ever helping women), would we still have capitalism...?
Or would the world be a better place?