Thanks for all your comments/suggestions. A few other thoughts:
1. Both Star Alliance and Sky Team have priority baggage handling for Gold members. This is explicitly mentioned on their websites, and I have always been given priority tags on either of these alliances as a gold member, even flying economy. Granted, this may not translate into faster delivery, but it is at least a promised benefit.
2. Agreed that the priority label may not help, but it shouldn’t do any harm and I would have thought (maybe wrongly) it is better than nothing.
3. Papillion, actually on AF and KL, I have been told on a flight that my luggage would not be arriving (due to a short connection from LHR, undoubtedly). Still doesn’t help that you arrive without luggage, but at least you can march straight to the helpful staff who can sort you out and send you on your way rather than wait for the entire 747’s hold to be emptied.
I guess I am just looking for clarity of what is offered on BA. I would also like to take up the actual carrying out of the “priority” treatment, but that is for another time.