... and the part I do not agree with is the contention that a "slightly more patriarchal" society is better. That all depends on how one chooses to interpret what constitutes a "great" society, and as always, Baldur, you conflate "good" with powerful, and "prosperous" in general with prosperity for the few; and "what works best for everyone" with what works best for the most powerful. If we change the definitions of those words and make them less euphemistic, like great = powerful, plain and simple, then maybe we can come to greater agreement on that.
All societies that have power imbalances of any sort are not good for the majority. They result in an underclass that separates into different factions based upon demographic groups (race, gender, age, ethnicity, religious beliefs, tribal affiliations, etc.) and competing against each other for the greatest share of the power within their own class rank, which is a very nominal form of privilege that amounts to the greatest share of the crumbs or the trustee of a prison population. That is precisely what is going on here now with the SJW nonsense. Instead of many women striving for equality any longer, they are now trying to move past that and gain entitlement, while rationalizing it by claiming this "makes up for" past injustice. In actuality, equality for all makes up for that; nothing short of that, and nothing beyond that.
In actuality, our system has long been a kyriarchy, with different groups in the underclass experiencing oppression or privilege depending upon time, place, and circumstances. For instance, men are allowed more sexual freedom than women without being morally shamed for it; however, on the other hand, men are far quicker than women to be seen as guilty of sexual abuse when accusations are made, since women are viewed as nurturing and non-aggressive sexually, while men are viewed as hyper-aggressive and predatory. Men were traditionally given the power to make all important financial decisions for a nuclear family unit; however, men were also given sole blame when things didn't work out for the family in that sense. Women were often denied seats in politics; however, men were expected to fight all of the wars. In other words, in some senses, women were indeed oppressed; whereas in other ways, they were coddled and given disproportionate degrees of deference. The goal of SJWs of both genders is to retract the former while enhancing the latter, rather than going for true balance. Rights without the attendant responsibilities of empowered people inevitably amounts to power over those who are not given a free pass on responsibilities.