BA has a host of quality people who do a fine job for the airline and who are not always appreciated. But the same goes for most large companies. It would be a bad move for pilots to strike - it will only prove (as far as they were concerned) to management that pilots are a bunch of whingeing wasters, and in future their fine efforts will be demeaned even more.
No, a more mature and responsible approach would be better at the moment. BA needs all the help it can get in a number of areas. Top management is close to getting a bunker mentality, and no one would benefit if they do go that way.