This is very dangerous for the world. If anyone should be allowed to marry as many people as they want there would be a lot of society anomalies.
Also, due to the fact that sexual activity is something that transfers a lot of diseases it may create pandemia or something that would infect the global population.
Are you not confusing promiscuity with polygamy? The whole point of marriage is so they don't go to other partners, and precisely avoid what you describe. Else they wouldn't bother with marriage at all.