No one wants to go back to a situation where if you have a pre-existing medical condition you you can be deprived of coverage. No one wants to go back to a situation where if you get seriously ill you can get thrown off your insurance. Seniors don't want to go back to paying more for their prescription drugs.
The state's interest in marriage is stability. Generally speaking polygamy does not work for stability. Inherent in the whole polygamous movement is a deep and abiding misogyny and denigration of women. So polygamy is objectionable on lots of grounds.