Polygamy in evolution is used to spread the genes of a dominant male through multiple wombs, enabling some of the fittest offspring to survive. Polygamy in historically backwards societies enabled dominant males to send massive numbers of young men into battle, and accept massive loss of life, knowing that the dominant male could repopulate with many wombs. As we move towards a more complex and egalitarian society, polygamy makes much less sense. As we move towards a world where intellect and diverse skills matter more than alpha male traits, polygamy again makes much less sense. So, polygamy is both evolutionarily and culturally regressive.
From the standpoint of the rights of women and children, polygamy has always been an arrangement of coercion. Older wives displaced by younger wives, younger wives bitter at the favor shown to the children of the older wife. So polygamy is also regressive from a feminist standpoint. The cultures that currently practice polygamy do not respect the rights of women or children. OTOH, Polyandry would not be something most women would want, because who wants to pick up that many socks or watch that much golf? Women tend to be wired a bit differently that way, so although everyone is saying “why not polyandry?” the answer is that most women are not interested, and neither are most men.
From the standpoint of single men, the wealthy man who takes all the wives would leave them without sexual partners and therefore open to the pursuits of sexually frustrated, enraged young men everywhere…violence and crime. Or possibly sitting in their underwear hacking secure websites. Either way, if you see the gender imbalance in China and the problems it causes for rural men or men with less financial worth.
Polyamorous groups, if married, would create an undue burden on legal and financial instutions. Who will get the social security? How many adults get placed on the family insurance plan? Who gets custody of whom? The government does not need these problems. I also forsee scam artists using poly marriage for visas, entitlements, tax advantages, and financial aid. One big happy EBT card. How about one plus one for legal marriage, and then live together all you want?
Finally, we can’t judge the sexual practices of others, and that is not really the issue. No laws will stop people from pursuing what ever sexual partnerships they desire. However, marriage has never been about personal good. It has always been about societal good. So, I think that marriage as a legal societal unit should remain between two persons.