Also, artificial insemination is actually a pretty easy thing to do from a tech perspective, so you could consider sex to be an entertainment-only activity, rather than something done to produce children.
One of the important things to remember is that when you get into AI technology, you're able to gender-select, so your 20% would go out the window (unless you're dealing with a culture that prioritizes females to the point of infanticide).
Even in dairy cattle, you're able to purchase sexed semen to select for heifer calves (industry standard is 90% accuracy), and use conventional semen for your beef cattle for a 50/50 split.
But even as early as the 1980s, researchers were able to differentiate between X and Y-chromosome-carrying sperm cells in rabbits. It took another few years to be able to segregate the two types of cells, and then a few more years to work with IVF technology.
So if 20% of the population is male because Some Big Disaster Happened Killing Off All The Guys And Things Aren't Normal Yet, that's one thing, but if it's because 8 out of 10 babies being born are female, because Plot, giving them access to AI technology is probably going to cause more problems than it solves. (Unless, again, infanticide.)
But why would women want to enter into that sort of relationship?
--Historically speaking, women enter into polygamous relationships because of high mortality rates. Life was short and brutal, so the clan would band together for their mutual survival-- ie, if A was killed, A's wife and small children might be absorbed into his brother's or his father's protection. In practice, few except the richest and most powerful men were economically capable of supporting three or more women/households, even if the law permitted infinite wives. In some cultures, the law would actually restrict how you kept your senior wife + junior wives-- the households had to be kept roughly equal, rather than spending all your money on your favorite wife and then making your other ones subsist on chicken feed.
Often times, because polygamy (3+ wives) was concentrated amongst the elite and powerful, it was a way to control the spread of wealth, land, and power. Rather than diluting it, polygamy would concentrate it.
In the modern era, however, polygamy is mostly found in poor, rural cultures, such as the
Igbo of Nigeria. (Colonial-era anthropologists recorded that most men had 3-5 wives; the most powerful men had over 100.) "Women were considered sensible investments" (because they came with a bride price) "and reflected the man's social standing." But some women were married for interventive reasons--- ie, marrying someone else's widow so that she would be cared for.
The women went along with it, because the man's social status was her social status as well; women didn't like being the sole wife, because they found it humiliating to have the entire household on their shoulders, and they wanted someone to share work and keep company with; or they could be in a vulnerable position, and marrying into a powerful household would solve their problem.