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.

Polygamy: An endeavour to get more out of life than there is in it.

No Congress ever has seen fit to amend the Constitution to address any issue related to marriage. No Constitutional Amendment was needed to ban polygamy or bigamy nor was a Constitutional Amendment needed to set a uniform age of majority to ban child marriages.