But women already have a very loud voice regarding what our society will turn into. We're aiming for a Sapiarchy, rule by all Homo sapiens regardless of gender, sexual orientation, ethnicity, etc., as the natural extension of classical liberal principles. Yes, it's taken two hundred fifty years to get only partly there, but I don't understand the motive to try to trash that and go back to a less-diverse set of leaders. There's abundant research that diverse groups make better decisions. Not women! Diverse groups. Here's an example: https://insight.kellogg.northwestern.edu/article/gender-diversity-successful-teams

To the extent that our lives (on average) have gotten better over the past three hundred years or so, the non-technological causes almost all involve the classical liberal embrace of individual rights and the inclusion of a wider set of voices as full members of society. If you are arguing for this to go backwards to a less-diverse set of voices, then you need a much more compelling argument than that female-led companies currently do better. We don't really know why they do. Maybe the well-structured companies are more inclusive at all levels, and therefore have a higher chance of appointing a woman CEO, and it has nothing whatsoever to do with the difference in leadership. Maybe if it's meritocratic and women are about the same as men, picking 9x more men than women is a bad strategy because a lot of really good women are ignored in favor of not-top-tier-men-but-we-ran-out-of-the-good-ones-oh-well-I'm-sure-Bob-isn't-too-awful. Maybe women, in our current culture anyway, actually are fairly likely to possess important leadership qualities that men are unlikely to possess. These things could perhaps be teased out, but we don't really have them carefully worked out yet, and it's a moving target anyway because cultural context has the potential to change the behavioral characteristics of men and women, and to some extent what is effective leadership.

To the extent that our lives have gotten worse over the years, it's almost entirely due to our separation from nature, our separation from each other, and our embrace of capitalism as a resource-extraction method that is perfectly happy to extract as much labor from us as individuals as possible while giving us as little reward as possible in return. This is a very difficult problem which is largely orthogonal to patriarchy, save that in a fear-based hierarchy, fear can motivate capitulation to unreasonable demands of labor/reward exchange that wouldn't agree to if one were free to choose. But this is not the bulk of the problem. Matriarchy has no answers here that I know of, save possibly that it leans harder into the social safety net that was already implemented by tamed patriarchal structures. Anyway, we've been rather less effective at taming capitalism than patriarchy. But much like dominance hierarchies, capitalism is the dominant system because everything else has thus far failed to scale to large systems without extraordinarily awful failure modes.