To say that priority tags have 'no impact at all' is not entirely true. I have on two occasions flown to MIA from LHR and both times the first 20-30 bags that came out were all priority tagged (after which I left with my suitcase) so it will have saved me a fair bit of time.

I would suggest though that it probably only works when flying directly longhaul from London to your final destination, and even then it will vary significantly by airport.