True, but when you consider that the cost of educating a child in the state sector is about £4,500 a year. The fact that the average school fee is about £14,000 means that effectively you get £2,800 discount as VAT is removed, then private schools don't pay business rates ( which the giv is now going to charge schools) and other taxes, so in effect the saving isn't that much.
Your logic is flawed. If you increase the fees from 15k to 17k (to pay 3k of tax) and I stay in the private school then the state would gain 3k.
But if you increase the fees from 15k to 17k and I leave the private school (which I and many other parents would) then the state is down by 5k, for educating each of my children. (Secondary spend is 5k around us).
My guess is that the tax gained would not counterbalance the costs of kids returning to the state sector and private schools going out of business. There are way too many parents who are only just managing to afford private education for whom an extra few k would be the final straw.
Now combine tax on private schools with re-introduction of grammar schools. Guess how many private school kids will be coming back to the state sector, taking away yet more grammar school places from less wealthy/educated families.