They, the children get a better standard of education because they are not moving; school, exam board, friends, even education systems as in the case of Scotland, every 18 months to two years. I had three cross border and one overseas posting whilst my children were at school, had they not been able to be at one school their education would have been totally compromised. There are no state boarding schools in Scotland, because whatever you say there needs to be a grandparent/relative nearby to deal with exeats and half terms.
You also totally forget the pull through value of CEA; no middle grade officer, 40ish,(the majority of ORs leaving point) two children 10ish, at least 15 years to serve, would contemplate staying on at the cost of his children's education. At that stage he/she is pensionable why would he/she stay. The Army has to show that there is a way to stay on that will also support the children.
Yes, the rules must be strict and be audited very robustly.