I will say that there was one instance a few months ago where I think the priority tag actually mattered.

I was flying COS-ORD-ATL and we were delayed on the ground for about an hour at COS which meant that I was walking up the jetbridge into concourse F at ORD when the flight to ATL was already boarding in concourse C. I decided I didn't want to try to run it considering I had a checked bag and was sure it wouldn't make it.

I went to the RCC to work for a few hours until the next flight to ATL. When I got to ATL, my bag was waiting for me in the baggage office. I still have no idea how my bag made it! I was shocked! ^