I tell the same to my students here, who are often getting the UT license in addition to their NV. In NV, the sign (if any) on a church does not have weight of law. In UT, it does, and the church can also register with BCI in lieu of posting a sign. As you mentioned, only the LDS Church has done so.
I find it odd, myself, considering how patriotic and freedom-loving most Mormons are. But they are also heavily involved in local politics, and, well, a politician is a politician. I'm sure he is only thinking of the children, after all.