Except that such a thing only took place in the past 4% of history after patriarchy arose. For most of human history it wasn't a problem. And no, patriarchy is social science term that describes a society with very particular characteristics - which you ought to know by now since you read me enough.
And, it's historically self-evident that men crafted a culture where women were essentially property, with almost no rights or power, where they were passed from father to husband, often with no say in the matter. A mere 50 years ago men had hundreds of more rights under law than women did. The term "rule of thumb" refers to the size of a stick that a man was allowed to beat his wife with (not larger than his thumb) will into the end of the 1800s. Spousal abuse wasn't illegal until 1927, but it was almost never enforced until the 1970s. Marital rape wasn't a crime in all 50 states until 1993. Yes, women participate in upholding patriarchy in many instances, but it's making up a fairy tale to act like women have not systematically been abused and disenfranchised - and that they often still are - because the time when that was legal and normative is not that far behind us.
And no, patriarchy did not "evolve" because it had more to offer. It was a cataclysmic onslaught that actually brought civilization to a standstill for many, many years. It spread because it was so disruptive.
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.
This is what the term patriarchy actually refers to from a social science perspective — a male-dominated social hierarchy established and maintained through intimidation, coercion, violence, and fear. The war chieftains who are the most violent and most ruthless rise to power and prestige, and an ethos of Might Makes Right prevails. Culture becomes more authoritarian and much more hierarchical and stratified. Women and weaker men are at the mercy of the domination and violence of the stronger men. For the first time in human history, some people count and other people don’t.