Think of it this way: If bigamy was legal, you would still want to at least know if you were the only spouse or one of several. A lack of reliable and readily accessible records makes deception all too easy.

Marriage is a contract. Agreeing to a mutually exclusive arrangement only to find out it isn't is a problem, even if you don't think polygamy should be illegal.

I don't know what percentage of the time bigamists are deceiving their spouses and married to someone else "behind their back," but that's certainly a version of events that happens and it makes everyone involved pretty unhappy to find out they aren't the only one.

This is typically done by someone who travels for work. It was much easier to pull off before our current state of global communications.