You have a point there, the union between the man and any of the individual women would be meaningless.
More than one wife at a time is not recognized in most countries. It's only the Middles Eastern countries that practice multiple wives. And they are mostly nothing but chattel.
Only the first wife has any status there, but divorce is simple and no paper is required. All it takes is for the man to say, "I divorce thee," three times in front of two witnesses.