Polygamy leaves a very angry pool of low status males. Not very good for those in power
“Since I have been preaching…that a man should have only one wife I have not been well received by the women; for, since they are more numerous than the men, if a man can only marry one of them, the others will have to suffer. Therefore this doctrine is not according to their liking.”
One possible hypothesis is that polygamy itself is the cause of this: the higher competition for wives drives the men to extremer forms of acquiring status (war, hunting, etc).
Of course, one doesn't need to condone polygamy to see this phenomena occur... liberalized divorce laws will suffice. you just spread the polygamy out over time. That is, when there is nothing shame in dating/marrying a divorced guy, you'll end up with a smaller and smaller percentage of men getting women, and a larger and larger group of men living in their parents basement hoping that some woman -- any woman -- will swipe them on tinder. This cohort of young men will prove to be very detrimental to society.