I think that making it illegal has opened the practice to a lot of abuse; underage girls being coerced into marrying old men, boys being kicked to the curb so they don't become a rival to the established males, trading of influence, etc.  If it was in the open the abuses wouldn't be eliminated, but most probably greatly reduced to about the rate we see in 2 person marriages.
In the end, as far as the state is concerned, a marriage is just a contract between two parties.  Why can't the contract be between more than two parties? Like pretty much all other contracts.