I think the main problem that the U.S. government has with polygamy is not so much one of beliefs as that *some* polygamists produce a lot of children through plural marriage and expect welfare to foot the bill. You could argue that this does hurt people, by depleting the social services network that is there to help etc etc.

However, I think that they're going about it in entirely the wrong way: if plural marriages were legal, then the state could feasibly set boundaries and guidelines, i.e. you can have as many wives and children as you can support without relying on social assistance.