It’s true about the stamp duty, but when they sell the house one day they will make a good profit and not pay tax.There are property millionaires sending their children to state schools in London.
As to your next point I completely agree that there are both free and fee paying schools in affluent leafy suburbs. But the fact there are private schools too does not make it a myth that people move to them to get school places at sought after free schools, including free grammar schools ( which not all areas have the privilege of having.)
Look at estate agent blurbs. They will always mention a provision of good schools of both kinds as a selling point.
Meanwhile some people live in poorer areas with less good housing in order to afford private schools. Some parents may choose to down size/change area to make the difference to afford the vat. Bursary children could be living in very much less well -off areas.
We all need well educated children. Education is never a ‘luxury’.
We should all be paying more tax to the pound, if we are above a certain income, including those called working people who earn a wage above a certain income, in order to provide good education for the country’s children.
It is wrong that the people now being charged vat on school fees for their child’s education have already paid tax and also already save the country £7500 per annum per child/ over £100,000 per child over 14 years.