We're still talking past each other.

I'll try again.
1) We don't know of any truly female-dominant societies. That's what the wiki says and that was your own starting statement in this thread. All societies known to us range from "sexes are about equal" to "males are strongly dominant". I hope we agree so far?
2) This being so universal, underlying reasons are clearly biological/evolutionary. Males must have some biological advantage over women. Obvious (and probably only) one is strength, further amplified by how our way of reproduction limits physical exertion of females even more.
3) This advantage obviously manifests in many different ways. The ability to settle intersex disputes in male's favor by force or threat of force is just one among them. I'm certainly not claiming this capacity for violence is the most important, let alone only aspect of it. You have yourself explained another mechanism. I'm sure yet others can be found. I'm not disagreeing with your explanation either. I'm just saying that "being better at punching things" and "being better at carting grain to market" both come down to the same underlying reason - males being stronger. Neither "emergence of family as an unit of production" nor "development of intensive agriculture and large-scale exchange" would have translated into male dominance without it.
4) Males being stronger does not "directly or straightforwardly translate into social power over women". That is a claim no-one has made. After all, we started with pointing out there are societies where sexes are about equal. However, males having this one comparative advantage and females having none means that emergence of social order where females are dominant over males has historically been that much more unlikely.
But my initial claim was that,
I don't know who far "who can beat who to death" is sustainable as the organising principle of a society.
1) No fundamental objections to this one, although if we're going to be picky I'd argue that plenty of societies are female dominated
within the right context. Even a lot of patriarchal societies take on a strangely matriarchal bent within the boundaries of the household. There's a reason that the hen-pecked husband is a stock character across so many different cultures. This stuff is always contextual and negotiated, and from the perspective of those living, usually understood as
practical, however historically-limited their assumptions, it's not about the exercise of power as an abstraction. As I've said, what we call "patriarchy" is in practice asymmetric dependence, and that still assume interdependence; very men in any society are actually independent of women, at least not unless they've been rendered more deeply dependent in some other way.
2) Why do we assume that the biological explanation lies simply within human beings, and not within, say, grain crops, or herd-animals? Any human society with a more complex lifestyle than hunter-gathering is part of a project comprised of several and perhaps dozens of species, however enthusiastic or conscious we treat each participant, we can't treat human biology as something discrete and self-contained in that context. Even before we get on to the question of what aspects of human biology may tend towards male domination.
I also dispute the framing of "advantage". That implies competition, but men and women are not naturally placed in competition. So far as biology is concerned, men and women are squarely on the same team against a hostile world. It requires an already-existing patriarchy for an "advantage" to realise itself as such. This framing rests on the assumption that one gender will naturally attempt to exert power over another, and that men are just better at it, but that assumptions has no clear basis. That isn't just pedantry, it's an important part of how we conceptualise this whole question: whether gender inequality is a product of gender conflict, or whether gender conflict is a product of gender inequality.
3) What is your reason for believing that the strength of men was routinely used to settle disputes between men and women? We're not talking about a hypothetical Atlantis, here, we're talking about human societies as they actually developed. One of the overriding concern in all societies is minimising violence within a community, whether this is through the state or through tradition or through a single overriding personality. Even if the solution is to ritualise violence, as in a dueling culture, or by the threat of violence, as in an authoritarian society, the intention is to minimise the actual use of violence. A society in which people routinely resort to violence to resolve their problems is one which is failing, which is well on its way to being something less than a society. It's unclear why a greater capacity to disrupt society would make men more powerful within society.
Further, as Owen pointed out, why does strength only become an important factor when we're specifically talking about the relationship between men and women? Rich men are not necessarily strong men than poor men. Old men are, generally speaking, weaker than young men. Priests and administrators are very generally weaker than warriors and labourers.
4)That claim was essentially a rewording of my initial claim,
I don't know who far "who can beat who to death" is sustainable as the organising principle of a society.
If nobody disagrees with that claim, why have we spent five pages talking about it?
As I've said, I don't even dispute that human biology does play a role in gender relations unfolding as they did. What I dispute is that strength is really all that central- especially given that "strength", here, only really means "upper body strength"; pound for pound, women generally match men in lower body strength, core strength, or endurance. The male "advantage" is only consistently manifest from the pecs up. What I argue is that a far more fundamental distinction between men and women, the reproductive cycle, ticks every box required by the appeal to "strength", and has the additional advantage of actual explanatory power.
What puts men in this position of asymmetric dependence in relation to dependence is more than anything else mobility. Men can range freely and for greater distance from childhood to infirmity, where women are often constrained by pregnancy or nursing children. That is inevitably going to inform the division of labour far more deeply than how can bench how much. Men don't actually need to be stronger, could even in principle be
weaker, for society to unfold broadly as it did, for the division of labour to develop broadly as it did. The genetic-level difference is not so profound that it will remake the heavens and earth. Between any two random individuals, nutrition and lifestyle will count for more than genes. Even in a society where those characteristics are relatively uniform, the strongest woman will be stronger than the weakest man. But pregnancy, and the consequent differences in mobility, represents a more general condition with less variation between individuals, so far as this question is concerned.
The problem for the "muh genetics" school, as I've suggested previously, is that pregnancy is not just something that happens by itself. It is something over which women exert a certain degree of control even from very early times. It undercuts the biological inevitability of patriarchy, and places it as the unintended consequence result of a series of thousands of years of human decision-making. It turns patriarchy into something that humans built, and can therefore demolish, rather than something that happens of its own accord, and which we can at best hope to repress.
No you don't. You just have to assume solidarity regarding come issues among men. Only that, no more. And we do know that humans, whether men or woman, do have group solidarity where their interests align (or are threatened). That is not specific of men, it is a feature of social groups - it actually defines social groups.
Why would we assume solidarity among men?