Marriage is a social construct which existed long before the notion of a "legal construct" was even conceived. I am unaware of any evidence that, in the entire history of the world, more than a million people total have ever lived in societies which did not award particular recognition to marriages involving exactly one man. Most societies have required that marriages have exactly one woman, but that requirement was nowhere near as universal as the requirement that they have exactly one man.
If marriages not involving exactly one man would be beneficial to a society, there'd be some evidence of that. There isn't.
Keep in mind that even in societies that allowed polygamy, the marriage was still considered to be between the man and each wife INDIVIDUALLY - each wife did not have some kind of marriage relationship to every other wife. Marriage was still one man/one woman even in polygamous cultures.
The fact that marriage is treated uniquely in society BECAUSE of what marriage is in its essence is the basis of our marriage laws.