The problem is the religious nut case part, which often leads to the reality being very different from your rosy hypothetical. In real life, polygamous relationships often involve older men with young, often underage, women who have been coerced into the relationship and are often sexually abused. I have nothing against polygamous relationships among fully fledged consenting adults. But that doesn't seem to be what most polygamous relationships are.
I could be wrong. I haven't done extensive research into this. If you want to convince me, show me the data.
You realize the data is scarce because the phenomena hasn't been studied, right? You seem to be hung up on the Sister-Wives nonsense and see it as the only viable data point in a truly unanalyzed section of human behavior. The fact of the matter is that I personally know people who are polyarmous and none of them are the creepy Mormon/Branch-Davidian type. Most that I know who are poly are queer (like myself) and far from religious.
If anything, it should be you that should go and create a research program analyzing the nature of poly relationships in humans and the underlying causes, not me. I merely pointed out the reality that our law should consider accommodation for those individuals as it does for others. All you seem to be bringing to the table is scare mongering that depends more on the tiniest of slivers of human society for the proposition that poly relationships should be illegal. Such a proposition is not tenable on it's face nor in its contents thus far. Or in simpler terms: please do your own research because I'm not here to convince you either way (but you seem damn sure to convince me that my poly friends are some evil bad fundies wanting to rape children).
Edit: sorry for the rudeness. I take things personally sometimes.
Given it's illegal most everywhere, data is hard or little to come by.
There are two large groups: one with a pretty 'dirty' record regarding abuse/child marriages and another with a clean record. So this could come down more to an environment/community issue than a polygamy issue where, in one community/environment, abuse and child marriages are largely the norm and the other it isn't.
Warren Jeffs' Fundamentalist Church of Jesus Christ of Latter-Day Saints && Apostolic United Brethren. The former having the bad record and the latter having the clean record. (&& being the separator to avoid confusion) The former is larger than the latter but the latter is the second-largest church that practices polygamy.
E:
The burden of proof is also on you to prove that polygamy leads to abuse/child abuse as you are the one making the claim. Given there's little/no data to support either side, you'll have to wait for more research. Which would likely involve legalizing the practice and conducting studies.
I could be wrong. I haven't done extensive research into this. If you want to convince me, show me the data.