The Mosuo are not a matriarchy. They are a matrilineal, matrifocal culture. If you’d actually read this story instead of rushing to make your comment, you would have noticed that I reference the Mosuo.

“For the Mosuo of China, it’s typical for women to handle business decisions and men to handle politics. Children are raised in the mother’s household and take her name. There’s functionally no such thing as marriage or even fatherhood, although men living in their mother’s houses help to raise the children of their sisters and cousins and are much more involved in their day-to-day care than is typical in the West.”

As I already specified in the OP, a matriarchy would be a dominance hierarchy in which women oppress men. The Mosuo, just as with every other matrilineal/matrifocal culture that has ever existed believe in balance. Men are not second class citizens. In fact, in that culture they hold the political power. This would not be the case if it were an actual matriarchy.

You are correct that matrilineal/matrifocul societies were the default until just a few thousand years ago when patriarchy appeared. But, as you probably are already aware, those cultures were characterized by egalitarianism and cooperation. With patriarchy, you get not only men in power over women, but class systems and gross wealth disparity as well (a dominance hierarchy) - things that did not exist under the prior social system. If you had a highly stratified social system where women had the vast majority of the social, political, and economic power, that would be a matriarchy. But as I've already pointed out - that has never existed.

As I said in the OP: “ There is, however, a rich history of matrilineal, matrifocal cultures, where women, and particularly mothers, are revered and honored. These societies are not dominance hierarchies though. Each one displays a noted sense of balance and mutual respect.” That is the most salient point.