I think you're misunderstanding the problem.

Communism is actually a pretty great system of government on a small (tribal) scale. A kibbutz is basically communist, minus the ideological political philosophy (and often plus some religious ideology, though that varies...it does help, though). But it doesn't scale because the psychology of small-group interactions is not the same as the psychology of interactions with strangers. And for good reason: the game theory isn't the same either. In a kibbutz you can solve the free rider problem with social pressure and, in extreme cases, shunning/exclusion.

Now, you could say, well, just have a whole bunch of kibbutzes. But that doesn't work, because if free riders get ejected, they can just travel to another kibbutz that doesn't know about their reputation and start free-riding again. So now the bunch of kibbutzes either have to be fiercely xenophobic (sounds great, right?!), or they have to implement a distributed reputation system. Good luck with that! You can check Mastodon to see how that's worked out--transitive ban lists, inter-instance feuds, etc. etc.. Meanwhile, the patriarchal Twitter, despite an mind-numbingly long list of missteps, shows no signs whatsoever of being threatened by Mastodon.

You can't just wave your hands and declare "strong indications it would work fantastically". Communism is a strong indication it would be an abject failure degenerating very rapidly into dictatorship or worse. Now, it might be a benevolent dictatorship for a while, but although Communist countries have at times helped their people, the only one I'm aware of that has a claim to not have ever been strongly authoritarian is San Marino. Which is tiny.

It's a genuinely really tough problem when you try to scale. We don't really know how Catalhoyuk solved the problem (we also don't actually know how hierarchical they were, though it's a good guess that they were pretty egalitarian). And, very probably, it was smaller in population than San Marino.

So, a largely gender-egalitarian society with a pretty strong hierarchical structure which is carefully organized to be difficult to abuse and to provide advantages for the people in society and to promote equality? Sure. Makes sense, as long as you have adequate technology to not rely critically on either men's strength or women's reproductive capacity for survival. We already have very close to that in Sweden. "Yes, just do Sweden, but a bit more." Hardly revolutionary. Liberal democracy with socialist leanings (and first- and second-wave feminism) already got us there.

But can we get a matriarchal society (that isn't just Sweden-plus-a-bit) that isn't sunk by free riders or conquered by vicious bad actors (see, for instance, ISIS, the Taliban, etc.--if you're assuming global peace, well, first get global peace and then let's talk)? Let's experiment, but really, if it were that superior, companies that implemented it internally would be beating the pants off the patriarchal ones, and that's not what we observe.