My priority tagged bags come out very late in the game on more than half my flights. All flights between MDE-MIA, which are half my flights right there, they are always near the end. For my domestic connections, I don't think my results are any better than somebody without priority luggage.
I'd be just as happy if they got rid of them. Having them and then not getting the service annoys the heck out of me. I still won't get priority service, but maybe I'll be a little less annoyed.