What may happen is that BSA will be cut back so that it returns to it's original idea - to provide continuity of education for children who's parents are subject to frequent moves around the county or internationally, and where both parents are required to relocate - not just where the Serviceperson gets a draft/posting order, the partner stays in their current location, and the child is packed off to boarding school. What has happened over the years is that many people have abused the system to put their children into boarding school for the minimum time, then removed them to a local day school at public expense, which was never the intention. In addition, the allowance may be restricted to certain schools (again, the original idea) that are approved by the Forces Education people. The fees would be standardised (rather than ramped up to what the schools know they can get away with claiming), and the potential for fraud would be removed - BSA is one of the highest-grossing areas of fraud in the Forces, ranging from false bills, inflated bills, and in at least one case that I know, collusion and production of a bill for a child for two years after that child had left the school and returned to the public sector!
If people weren't abusing the system, then it would not be an open target for changes and reductions. Look at how many of the people who have their children in BSA-attracting schools have them there purely for the snob-factor of sending their children into private education rather than those who are genuinely away on postings. The RN is specatcularly bad for this, with a sea-going draft attracting the ability to apply for BSA, even though once the 2/3 year sea draft is over, and the wife stays at home, the BSA entitlement is continuing.