I haven't flown BA during the recent chaos but the last few times I did need to check a bag on BA out of T5 it was quickest to use the self service machines anyway - Club check in always had a queue whereas they were empty. Not that it seems to make much difference but the tags do print out with "priority" on them and I can't think of any other potential benefit of going to a CW desk!

Otherwise I would also concur with an outstation policy of Gold + J only. Somewhere like a Tenerife where you've got 48 CE passengers + all status passengers in one "priority" line is silly. Especially as in my experience these passengers spend much longer at the desk vs statusless ET passengers just dropping off bags