I also think that the priority tags have very little to do with when your bags will arrive but I think they do help to ensure that your bags do actually arrive. I have a friend who asks the agent not to put priority tags on his luggage when he is heading home to Sweden as he says that without the tags his bags almost never make it onto the last flight and then he doesn't have to carry them home himself and can wait for them to be delivered!! With the tags they make it home with him.