If BA were to start a scheme it would most likely be of the "mentored" type which is now quite common. That is, the student pays (with BA's pre-selection helping with the loan application) and, if performance on the course is good (probably VERY high standard required) and BA has vacancies when student graduates - then first in the queue.
Basically it costs the airline peanuts but they have some control over what the student does (mainly BA SOPS during the MCC course).