I don't know anything about Utah law or procedure.
I am not such a wussy landlord, but in California.
You are correct that the tenant is supposed to be out after a notice to Pay Rent or Quit expires (3 days or so). However, there are tenants who will be ignorant of the procedure and just wait for themselves to be thrown out. There are also tenants who know very well what they are doing and deliberatly act to take advantage of the fact that you cannot go out there and throw them out yourself.
There are many things that such tenants can do to stall the actual eviction, including appeals, going to Court again, creating other issues, challenging everything in sight. Unfortunately, there are also attorneys who will help them to do this, for a fee. In California, there used to be (probably still are) tenant legal assistance offices who will help a tenant to take advantage of every delay. This is not so much a matter of keeping someone from being "thrown out on the street" as to help them get free rent for several months.
Here in California, we have gained some help. We get a priority for a hearing, a strict limit on how long until a case must be heard, if unlawful detainer is proven, then LL is entitled to immediate possession (which means the order is immediately issued for immediate possession, Christmas or Yom Kippur or not), and we can ask for the defaulting tenant to deposit rent with the Court before any other delays are granted.
For the attorney, there is clearly an ethical problem here: To help the poor tenant not to lose her home until she has gotten thousands of dollars in free rent, or to simply tell her that she should have paid the rent, if not, now get yourself somewhere else to live and let this be a lesson...
Most attorneys want to help the poor starving, pregnant, aids-stricken, but environment-loving tenant to get away with the landlord's money, never mind the fee, and shame on the wicked landlord for his lack of sympathy. Fortunately, here in California, we have made some progress on convincing the legislature and the judges that tenants cannot be permitted to remain in LL's property without paying rent.
To answer your question about how long can this go on, the answer is potentially "for a long-long time".