The problem is that many people are ignorant of what is and is not in the bible, so if a group of priests teaches it, people will believe it to be in there.  In the end, you have the same problem, a book, interpreted by people convincing other people to do or not do things.  Ultimately, the problem in this case is religion.  Marriage in the US is a civil and legal event, if you want a religious wedding, you still need the state to give a license.