BA have done this in the past. I remember turning up to Gatwick back in 06/07 and them offering £99 upgrades on each segment for Euro Traveller - Club Europe, and I have seen them doing this at Newark a couple of times, again back around the 05-07 time frame.
Thing is, I think BA
's involuntary upgrade system (ie, only if required by Y/Y+/J being oversold) creates different incentives than those used more commonly in North America - where is seems the most senior elite will be upgraded until all seats in the front cabin is taken. If I were managing the BA
system, I would not do this often - it would end up cheapening the front cabins as people used to the offer would end up buying the cabin below and pay for upgrades - at cheaper rates than the true differential between the price of each cabin - at the airport.
A306, A318, A319, A320, A321, A332, A333, A343, A346, A388, B722, B732, B733, B734, B735, B73G, B738, B742, B744, B752, B753, B762, B763, B764, B772, B773, B77W, B787-8, BAe-146, Cessna Something, DC-10, E175, E195, ERJ145, MD-11, MD-80, PA Something