> and some version of polygamy becoming more normal
Polygamy arises spontaneously in societies where lots of men get killed off by wars. As soon as the M/F ratio normalizes polygamy goes away.
Fake-polygamy is like early Mormonism, where the proselytizers actively sought large numbers of women to rapidly increase the size of their group. Mormon polygamy mostly went away because of the numbers problem: it is unsustainable if you don't have a way to bring in extra girls or get rid of extra boys (the offshoot mormon cult in Colorado City sent boys away as soon as they hit 18 [2]).
[2] https://en.wikipedia.org/wiki/Colorado_City,_Arizona#History - Dateline or some other news shows had stories about teenage boys getting expelled from Colorado city, so that the girls could be plural-wed.
> with few men sharing many women (if you believe the online dating app stats and lots of anecdotes online).
Some men get more action than others, but this is mostly because they've learned how to not be obnoxious [3] about their interests, and go after the women who also aren't so interested in a relationship, or are good at tricking women into thinking they're long term when their intentions are otherwise.
[3] https://news.ycombinator.com/item?id=17554503
Women generally are selective about who they get with, whereas men generally will get with whomever happens to be interested in them. With that said, many women don't get hordes of men lusting after them, and some men have learned how to mesmerize women into their bedroom, then move on to their next target without second thoughts.
I posted previously about my friend who advertised on backpage for clients [0]. She was not full-service, yet was sort of traumatized by the experience anyways. She doesn't have problem with her catalogue of former boyfriends (entirely her choice), but she was bothered by the men who just wanted to pay for the privilege of putting their anatomy inside her anatomy without her being reciprocally interested.
Then there was the stripper I saw a few times... The last time I saw her, she told of how she gotten beaten up by strip club patrons who'd followed her home. She didn't feel safe at home anymore [0]. She was okay with getting random men aroused, but wasn't interested in sex.
[0] https://news.ycombinator.com/item?id=17810906
Offering prostitution as a service works for women who are flexible about who they'll get with; engaging prostitution as a client works for men who haven't figured out how to be interesting to women, or for men who are not interested in a relationship, or not capable of a relationship, or have other motivations (ex: I read about an Australian mom taking her disabled son for a monthly appointment with a sex worker).
With all this talk about legalizing prostitution, I think it appropriate to point out that lots of women are engaged in legal prostitution already, it's usually just called "acting". Some women pretend they're interested in a man, but they're more interested in their wallet ('trophy girlfriend/wife'). The other common not-exactly-prostitution work for women is pornography. The main difference between pornography and prostitution is men in porn get paid a token amount too. I'm sure many of the online porn producers were set up by men who just wanted to increase the number of women they boink without having to pretend to be interested in a relationship.
Some women do sex work because of economic pressure [1]. IMHO, a basic income of some sort would be an important part of any legalization of prostitution, so that the women who'd rather do anything else don't have to go into the sex industry to survive.
[1] http://www.taxiwars.org/2012/03/day-12-working-girl.html - this woman might not have had the ability to work in the US legally, on account of her immigration status, but we didn't actually talk beyond the formalities of her ride.
I intend to write a blog post titled "the predicaments of girls and boys", but haven't gotten to it yet.