4 school moves before I was 10 years old (none after as YWIW senior left the RAF) - family life was always a priority so we stayed together (I think he wanted the posting allowance!). So I and my sister went to local schools and learnt to fit in, tricky in Morayshire in the 70's as English kids were openly bullied, but not impossible.
My cousins went to Finborough (? SP) boarding school, their father was an NCO - having said that they could have gone to a local school as there were no moves during the school period of their lives - I always thought it was a bit of a cheek, as it reduced the pot of available money for those who did need it. But they seemed to survive on the stability.
In the end, it's a renumeration benefit that was offered and is now being altered / withdrawn. So worthy of discussion, but for my money going to local schools and moving every few years is pretty much what working life is all about. Mrs YWIW went through the US DODS scheme and also moved every two years to no great character flaws (apart from her liking for me) or educational defects.