I guess it's the same as with the Gold Greeting. On one day on a LHR-JFK, a 2500-3000TP GCH might be well down the order as the aircraft is full of GGL "commuters", but on another day on a LAS-LHR you might be at the top of the list.

Personally, I think the service should prioritise those that "need" it the most. For example, I would love to get a Jag from T5-T3 when my SFO-LHR is 45 minutes late, leaving me only 60 minutes to go through flight connections and get to T3 for my LHR-LIS. That helps both the passenger and the airline by avoiding misconnects. It would be nice to be able to expect this service in such situations.