Yes, that's largely established. But basically all more ambitious statements aren't established.

For example, we don't know if there is a biological given that would make people of some genotypes struggle to fit within those non-patriarchal cultures that still exist. We don't know to what extent non-patriarchical culture is compatible with acceptance of diversity--there really aren't good examples of any societies with both. We don't know whether large-scale societies can function without a nominally patriarchal organizational structure--again, no good examples. We don't know whether there were any non-patriarchal societies with lower rates of violence and other antisocial behavior than in the best-tamed patriarchal societies of today. And so on.

(Elle Beau always is quick to challenge people who think that "patriarchy" necessarily means male: in her academic circles it's an organizational strategy (usually but not definitionally run by males). I'm assuming, since you're linking her stuff, that you mean it in that way. Otherwise, we already mostly got rid of it in a number of countries--just look at Sweden, for example. We can do an end-run around all the arguments and just go: oh, hey, look at Sweden.)

It's quite worthwhile to explore alternatives so we can learn more about how we humans can organize ourselves. But everything does not indicate that a matriarchy would be better than a tamed patriarchy; we've been taming patriarchy quite effectively in some spheres for several hundred years now, and if you're going to allow that all the gaps in knowledge mean that matriarchy looks good, all the best trends in patriarchy-taming (e.g. rule of law, meritocracy, universal basic income or equivalent safety net, etc.) if extrapolated leave patriarchy with no serious problems at all.

(Incidentally, I did read the other comments and other people challenged pretty much all of Amanda's least-well-supported points so I wasn't going to bother to write a reply myself.)