BA's cost reduction program is based on legacy staff being around or a considerable period. However, the initial savings projected have been delivered. Indeed, I seem to remember that all of BA's better than expected full year financial performance was down to them achieving higher than expected cost savings.
BA don't need all legacy staff to go on day one, or even any time soon. The recent investor presentation forecast New Fleet would still represent a minority of crew in 10 years' time.
However, as wascrew has alluded to, if the hardcore can be persuaded to leave, then BA has the chance of speeding up those cost savings. Rejection of the latest deal gives BA both the means to speed up the process (if we believe the Ava story, commuters will be starved out soon), and some money budgeted for other purposes (pay rises) to pay off those that go and minimise the legal risk/cost. Speeding up the move to New Fleet brings forward the cost cuts. Again, some of that opportunity saving can be used to pay for higher cost staff to leave in the first place.