So, you know more than UNESCO, the Smithsonian and people who publish in Scientific American? 🙄 Give me a break . . . As clearly noted in the OP, greater sedentism, agriculture (and the jump in population density due to it) greatly impacted any inclinations for mass violence. In addition, incursions from war-like tribes like the Kurgans put an end to the intentional peacefulness of early Neolithic peoples. This isn't a theory - it's a statement of facts.
Go back and reread the OP - not to respond, but to understand - and you'll notice that all of your "concerns" have already been addressed. For example, it's irrelevant what non-human primates do, since it's well established that transcending our primate cousins dominance hierarchies is the central adaptation of human evolution. It's also well established that "social Darwinism" which has nothing whatsoever to do with natural selection - was a theory concocted by eugenicists, colonizers, and those seeking to justify the downsides of laissez-faire capitalism.
The one thing they all had in common was a dominator model of social organization: a social system in which male dominance, male violence, and a generally hierarchic and authoritarian social structure was the norm. Another commonality was that, in contrast to the societies that laid the foundations for Western civilization, the way they characteristically acquired material wealth was not by developing technologies of production, but through ever more effective technologies of destruction.
Eisler, Riane. The Chalice and the Blade (p. 86). HarperCollins. Kindle Edition.
