The argument for denying plural marriage is that, in the US, polygamy has been primarily a tool for subjugating women. Legally recognizing these unions would be granting legal cover to people like Warren Jeffs.

If this view is outdated, and our laws against polygamy are causing people real pain, then by all means let them make their case; perhaps times have changed. But we do not make laws in the abstract, and polygamy in the USA is intimately connected to subjugation, abuse, FLDS, and other ugliness.