Okay, lets completely forget the controverial side of this.
If polygamy was introduced, hundreds of people would try to get married at one time. Because after you're married once, you might wanna stay to marry again. And again. Nobody's gonna leave, and people are going to keep coming. Also, there'd be extra lag because it's not like when marriage was first introduced and you needed a dedicated partner; you could marry all your friends right? And all your new cool friends you're gonna meet in the future right? The cathedral will never NOT be laggy and it'd be difficult to get a marriage at all. So the LAT admins might have to install a new church just because they introduced this.
And honestly, are they going to go through all of that if little to none are actually a polygamist? Doesn't seem realistic.