It occurred to me that this is a strange example of the Theory of the Second Best. Suppose the government took a laissez-faire approach, keeping the roads open. If the Pope wants to get people off the roads, he has to pay them to stop driving. Obviously this encourages people to drive in order to be paid to stop to wait for his procession to pass. He could also simply refrain from visiting, but assuming the benefits from society of his visit are greater than the costs, this might be inefficient.
Given the inability of the market to solve this problem, the second-best (and very un-laissez-faire) solution is to simply ban driving in certain areas at certain times. The first-best solution might be to privatize the roads, if this were somehow possible.
The two crucial and questionable assumptions in this story are 1) there is no market solution available to the Pope and 2) privatizing the roads is possible and first-best. Maybe the Pope can, at low cost, take a helicopter everywhere he wants to go, making 1) false. 2) might also be false, if privatizing the roads leads to other market failures. I don't think this is necessarily the case, though. Shopping malls have private "roads" for pedestrians, and they work just fine. Some neighborhoods and businesses maintain their roads privately, although they not enforce traffic laws there. The real trick is how to get there from here.