

I’d argue patriarchy is a bad model for the social dynamics regarding sex. It’s just another rebranding of Marxist class conflict onto something other than economic class, and as a consequence it works about as well as that something actually resembles (or alternately is a proxy for) economic class. This means it works OK for race in the US (except for Asians, who get to be functionally white in some cases) but it it’s a bad fit for sex.
It’s why there are so many apologetics around patriarchy for all the myriad cases where reality just doesn’t seem to align with what you would expect based on it a priori. “The patriarchy hurts men too” is probably the most common, though you’d be hard pressed to argue “Capitalism hurts billionaires too” or “white supremacy hurts whites too” in the same kind of fashion. Because the moment you stop looking at the fraction of a percent of the top performers the idea that society was created by and for men to benefit men above women first and foremost just doesn’t align with observation.
What seems to be a more fitting model to me is malagency, the idea that agency is inappropriately assigned based on the sex of the party in question. Specifically that in general women are assumed to have less agency than they otherwise might while men are assumed to have more agency than they otherwise might. This fits neatly with lots of observations - ideas presented by a man being given extra credit or consideration than the same coming from a woman (because he’s seen as more responsible for his ideas than a woman might be), the very highest tiers of things having over-representation by men but also when men are also over-represented at the bottom (for example, rough sleeping homeless) because they are seen as more responsible for their own successes and failures as well, or why the criminal justice system treats men much worse than women (women are seen as less responsible for their transgressions). Etc, etc.
Generally, not absolutely at all times. The woman I eventually married settled into a plan of taking turns as to who pays for dates (she literally insisted to pay for the second date since I paid for the first, and it grew into a pattern from there). From the mid 90s to the first Trump admin (the period of time in which I was dating girls/women) she was one of only 3 who suggested or encouraged splitting the costs in some fashion.
Who put all women in a box? It’s a tendency, a trend, not an absolute descriptor of all individuals. At the same time if you believe wealth/status indicators do not play a significant role in how attractive women perceive men to be, or at least no more so than the reverse you’re going to be very disappointed in the ladies. There is research out there to that effect, specifically that wealth indicators correlate positively with attractiveness for both men and women, but that the effect is much stronger in women considering men than the other way around.