What is the ‘excellent’ education that is supposedly delivered at private schools?
It is exam results, not ‘education’ in a thought out sense.
Smaller class sizes help teachers get on the case of individuals more, and the kids make an effort because their folks are paying for it hence they are in a position to get the grades. In addition even in those circumstances some people pay for private tuition in some subjects, notably Mathematics, but the school will still claim the credit for the results if they are good. Many private schools filter at the start anyway, looking for those likely to get good grades.
The debate about the VAT is going on, but so far I have not heard the argument that private schools are private business that can (and some do) simply shut down just like that, as Debenhams did, or any private businesses.
When there is a system that private schools never ever close at the veritable drop of a hat, then there may be a case for looking at VAT or whatnot, otherwise people can pay up the fee including the VAT just as they pay VAT on a car or a chair.