Polygamy has been one of the greatest oppressors of women in all of history, particularly when administered by fundamentalists religions. Pedophilia, selling child brides, and abuse are highly linked to polygamy. It's bad for men too, since only the wealthy have access to marriage.
Marriage exists so that societies may have cohesive families in order to generate progeny. Allowing multiple partners within such a family would serve to increase progeny. Thus, it serves the societal purpose of marriage even better than monogamy.
This would leave some people dissatisfied and without partner. If there were 10 people (5m/5w) on earth and 1 woman married 3 men, 4 women must fight over 2 men. This may only work if receiving/giving polygamist parties are balanced in numbers.