I rather like the idea of having a harem of bodacious college-age sexpots, like Hef’s grotto. In practice, though, the vast majority of polygamous marriages are business arrangements between a rich old man and his underaged bride’s parents. It’s not something I would defend.
Marriage as an institution only exists in the context of the state, private property, custody of children, etc. so the “complexity” issue is a real one. If all you actually want to do is invite a bunch of your friends to live in the same house and maybe fuck each other sometimes with no other strings attached and everyone’s totally cool with it there’s no law that I’m aware of that’s stopping you from doing that right now? 
I wonder the same thing. The only thing I can think of is that it provides an opportunity for milking the welfare system for all it is worth! A husband could claim 10 spouses and 50 children as dependants in need of food stamps and incom assistance. But the matters of divorce and child custody and inheritance (concerns expressed by other posters) not complicated because even in polygamy it remains that Mike marries Judith. Mike’s four other wives do not marry Judith. In divorce, custody of mike’s and judith’s kids is granted to mike and/or judith if they are fit parents. Inheritance is the same if you have one spouse and 2 kids or 5 spouses and 50 kids…It is divided per the Last Will and Testament. Lacking that, it is divided thinly over the entire brood.
I don’t think so. It would be so if Mike marries Nancy and each of Mike’s other 7 wives also marry Nancy, but that isn’t what happens. Only Mike will marry Nancy and Nancy will marry only Mike. Their specific contract of marriage is between the two of them and no one else. Thus, dissolution of that contract is between only the two of them. If both Mike and Nancy are fit parents, then child custody is only between the two of them. Emergency contacts? No more complicated than that of a single parent who lists his mother, his sister, and his next door neighbor as contacts. Power of Attorney takes care of pretty much everything…married, partnered, related or not related, with regard to making medical and financial decisions. A Lat Will takes care of inheritance and if there is no Last Will…it goes through probate as it would in a monogamous marriage and everybody gets a tiny piece of the pie.