In one sentence you can explain why polygamous relationships should not exist for the common man and woman.

There is a great probability that the man and wives frequently can’t responsibly and financially help the polygamous family unit nor the offspring and a divorce means a great probable and unacceptable financial hardship on society!!!

For very wealthy billionaires and multimillionaries polygamy is a desirable custom if a very large government controlled escrow account is maintained so if a divorce exists then the wife or wives and offspring of the divorced male will have a secure financial future without becoming a financial hardship on society.