If it helps to put up with the 'stigma' of being on the 'hideous' short haul fleet at BA, every year you prevaricate and refuse SH will be one year less at the end of your career on Pay Point 24. At the current scales, assuming you get there, that equates to about £130,000 per year to refuse that SH slot.
Add to that the loss of seniority position and thus a delay to command as people have also pointed out and the scenario doesn't look so rosy holding out for the real pilots metal (
). If you go for the SH fleet, sit there for 4/5 years and then move to LH you take your seniority with you and will have a far better bidding position to avoid the constant east coast weekend States trips. Which, oddly enough, generally go to those holding a 'blind line' and are junior on the fleet.
Also, if they change the rules for those swimming in the pool, to extend the time you can tread water, those concessions will NOT be given to any pilot who has refused a fleet allocation.
Just a couple of helpful guiding points!
p.s. They are offering unpaid leave to ALL pilots, not just specific fleets so don't assume anything.