If the law follows no morals, there is not a single argument against polygamy.
Polygamy was morality dictated by the faith in the Mormon religion, which considers itself to be a Christian sect.
Are you saying that the State should have the power to dictate to the church what is or isn't moral?
Oh please polygamy existed thousands of years before Mormons. The state already dictated to the Mormon church what was legal and moral when the law forbid polygamous Mormon marriage.
If the State has no morality, does not dictate moral behavior and is amoral as state policy, there is no reason to forbid polygamy, polyandry or polyamory.