There might be a couple reasons people don't want to be a part of such things. You've described what is known in modern slang as "a clusterfuck." The term has negative connotations, describing a totally, completely screwed up situation.
clusterfuck
n. A chaotic situation where everything seems to go wrong. It is often caused by incompetence, communication failure, or a complex environment.
v. To fuck (something) up, to make a total mess of.
Make no mistake people want flexibility. They want to have more than one partner (and they do). They just use deception and infidelity instead of doing it within an honest relationship. Chaos is the state of marriage right now. I'd say when something fails for most people, its a total mess. The stats are on my side. People lie, steal, and cheat at a high rate. Divorce rate is beyond the critical point.
In nature what happens is 80% of the women go after the top 20% of men. This is a well known principal in science, one that is supported by studies as well as data scraped from dating sites. Essentially women largely overvalue their sexual marketplace value and only go after the top 20% of men. They see dating their equal as dating down, and dating down as men out of their league.
So the question is, since this is human nature, why would you support a system that works against it? Why not embrace human nature? I feel like you have said this in the past. Why not let the free market have its say?
Imagine there are 10 people. 1 man represents the 20% you mentioned. Maybe he can have sex witha all 5 women but there is no way he can please all 5 women in every way so they will eventually seek companionship from some of the other 4 men. If he can and they are all happy then what is the problem? Most likely, those women would either take a man in the 80% to themself or workout something polyamorous.
It almost sounds like you are a sexist socialist who says capital (women) should be distributed fairly evenly so that the 20% doesn't take more than their fair share. Strange how you are 180 from yourself on this topic.
Notice all the middle aged women now crying about how there are no good men left? You think that is a coincidence? All the men they COULD have paired with are no longer interested, because they have nothing to offer them with their primary reproductive years behind them. Instead of finding a man who would have stayed with them into old age during the years of her highest sexual market place value, she was busy trying to "trade up" and ended up getting traded in herself.
There is more reason for marriage besides building a family. Some seek companionship, some seek sexual plaesure and yes, some seek to build a family. Polyamory allows the individual to cater their relationship to their personal needs.
In many polyamorous relationships, the women can have sex with a man in the 20% to satify her fantasy within her marriage to a man in the 80%. The man can do the same and the two can live happily ever after because it was all transparent and conensual. Its the force sexual exclusivity that is actually tearing many marriages apart.