Well, for starters, a heck of a lot of the kids produced from the current illicit unions are on welfare. I'm not sure it's in the best interest of any kid to share his father with twenty or so other kids and a few other moms.
It's also a horrible, horrible lifestyle foisted on these women. What do you think those first wives feel like when they see their husband taking his next wife. Do a websearch on the misery and suffering of these women. It's awful.
Do you feel it materially different from this when a divorce happens in between?
Face it, America. We already have legal polygamy. The only catch is it has to occur serially and not concurrently.
When considering polygamy and the law, you must consider how illogical the supreme courts decision to make a man's religious duty illegal was then, and continues to be today. Let's examine this logically. When reading the dialect of the supreme court decisions you must note that emphasis is placed on order of the union over a man's religious duty. It is my intention to help you understand that the US government in it's infinite wisdom has attempted to create order for itself whilst endowing utter and absolute chaos upon it's blindly obedient constituents. To punctuate my case I point you to the fact that before this practice (aka: a man's religious duty) was made illegal, very tedious and accurate records consisting of lineage were maintained by these religious orders. For the past, nearly hundred years, as the government has forced it's unwelcome version of order upon it's citizens, written documentation has not been maintained. It simply could not be done, because documenting who your dad and moms were would pit the law against your parents. Therefore, our government; by creating what it considers order for itself is in fact creating substantial confusion and risk for it's citizens. Citizens practicing polygamy are limited to a family medical history of not more than two parents deep. To admit to more is to subject their parents (and possibly other loved ones) to risk.
U.S. Supreme Court, (1878), REYNOLDS v. U.S., 98 U.S. 145, taken from http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?court=US&vol=98&invol=145, on Thursday, November 30, 2006