The only time the Priority tags have helped me was one time on a regional jet where one of the 2 cargo bay doors was stuck closed - because of this, they couldn't fit all of the outgoing pax bags on the plane. Those with priority tags were guaranteed to be put onboard though - so my bags made the flight while some other pax didn't

I almost felt worse for the pax on the inbound flight though - their bags were stuck inside the plane for god knows how long!