I'm arguing that if sex is more casualized, which it is, then partners are not "competing"; they can have sex with Man A on Monday and let Jody from Accounting have Man A on Tuesday.

The failure modes for this system are twofold: if women want sex much less than men, by a huge factor (which for casual sex may well be true) or if the most desirable men are insatiable nymphomaniacs and quite capable of finding a spot for every groupie. I'm not sure if the second part is amenable to change, but I'm sure it's possible to increase women's libido because surveys tend to indicate women have much less satisfying sexual experiences than men do, so changing that would show room from improvement.