My understanding is that the the problem started because BA do not have enough staff to meet all their arriving a/c at peak. As it is good practice to leave the stand entry guidance (SEG) off until the person responsible has checked the stand for FOD, equipment, spillages and airbridge serviceability - and in BA that's the Red Cap. Following this procedure left a/c on the taxiway and crews and pax fuming.
Instead of devolving responsibility to others in the turnround team, BA approach BAA to leave all the SEGs on all the time. (AGNIS green?) so that pilots could pull onto stand and await the dispatcher whilst not blocking the thru route.
Now how that became "turn off all the taxiway green lights" I don't know.
An opinion from pilots about trundling onto an unchecked stand with the real risk of causing damge to the a/c or airbridge might also be useful.
BTW I know the name of the person in BA who asked the question - but dare not speak his name!
Sir George Cayley