One factor that I didn't see addressed in the post which does make a significant impact is that men in general rate women more similarly than women rate men.
As such, male advantage is probably a lot lower in the real world, if (hyperbolic) every woman has a different man on nr 1 of their preference list, and every man has the same woman as nr 1 of their preference list, all women could theoretically have their best possible partner, while only one man can.
See for example:
https://www.marketingcharts.com/demographics-and-audiences/m...
As such, male advantage is probably a lot lower in the real world, if (hyperbolic) every woman has a different man on nr 1 of their preference list, and every man has the same woman as nr 1 of their preference list, all women could theoretically have their best possible partner, while only one man can.