Well, to be honest, I think this is mostly a problem when these men are actually in exclusive long term relationships with multiple women. I’m not a fan of players; but there is no reason to believe they are robbing men of reproductive opportunities, precisely because they only date each woman for a few days or weeks and move on. Even if we calculate a year or two of heartbreak, that leaves plenty of time to have children with another man.
I would say that it is actually poverty, or to be precise a harsh socioeconomic climate with inequality in career and financial opportunities that causes polygamy, whether the law allows for it or rich men simply keep poor women as mistresses. In my mom’s country, you also frequently see a poor married woman having a rich, also married lover, in exchange for support. Kind of like how poverty goes together with prostitution.
The best single predictor of the incidence of prostitution is the degree of male income inequality. This applies to wealthy cities too - not just poor ones. So there is a link between fiat money credit inflation and the decay in morals of a city. Thomas Mann wrote about this in “Disorder and Early Sorrow” (in the context of Weimar Germany). The blurring of the line between amateurs and professionals during bubble time is striking, and has been discussed in various pieces on the Manhattan scene pre-2007.
With respect to the question of monopolisation of the reproductive potential of nubile women, dominant men pursuing this kind of strategy don’t just date each women for a few days or weeks then move on. A single man might in effect be taking several (and potentially tens) of women off the market for months to years. The practice is likely to be very different to the theory even if it is supposedly not an exclusive thing - by nature men have a much easier time dating multiple women concurrently than do women juggling men. And then after a fling with a dominant man, the self-assessed market value of a woman may rise, possibly to unrealistic levels. In comparison other men (who may be the more realistic candidates for a long term relationship) may just sink beneath her notice. Multiple flings may weaken the ability of some women to form a very durable long-term bond. So marriage is very much less appealing to a provider sort of man in our age than it would have been in a world with greater social and moral constraints, even without the changes in divorce mores and laws.
The above is controversial, and hardly aesthetically very appealing but seems somewhat founded in human nature to me.