The OP claims that this is a "clearly advertised benefit" so I would like to see where it is clearly advertised as a benefit.
I do not see BA advertise priority baggage as a benefit at all on their website or other sources.
Well, it's
clearly advertised on the baggage tags - you know, that big word "Priority" that sits prominently on the tag. Is there a definition of what that provides? No, but there is a reasonable expectation on behalf of the consumer based on what the word means in the English language. If they don't actually provide a priority service for bags, then they should ditch the tags and stop the pretence.