If there are schools out there where @TheBroonOneAndTheWhiteOne was bullied for being too clever then we are really in a massive mess.
Of course there are - it's called "othering". It could be red hair or any other physical trait, it could be a disability, it could be social class in either direction (like @Grumpyoldpersonwithcats had), it could be athletic ability. Children pick on anything they can as an excuse, and it's often done as a way of feeling superior in some way.
a policy which is likely to turn out very expensive to the taxpayer
A little confused by the logic here - how? Maybe the very low numbers of children added to the state schooling system, considering that approximately 6% of children are at private school and the loss of the VAT loophole is very unlikely to mean more than about 1 in 10 of these children transfer to state schools - the seriously rich will always be able to pay anyway. So still a decent additional income to the Public purse from the tax.
Then there's the question of what do the parents do with the extra money they now have which they aren't spending on luxury education costs - well they tend to spend it on other things which is good for the economy and adds to tax take from other items.
I do seem to recall for quite a while before the current government came into power many threads on here from parents crying about how they couldn't afford private schooling for e.g. their 3rd child because of the COL crisis and how unfair it would be as the first 2 were going to private schools already, or that they wouldn't be able to afford it for their precious new born etc. Hearing about a few smaller private schools going under. VAT was obviously nothing to do with that, it was purely COL crisis.
Chances are the OP's local private school has been struggling for a while with dropping numbers and rising overheads, the VAT was just one small factor.
And I STILL can't get why this is being called an "Education Tax". I went to a private junior school then state grammar. I think the biggest differences between the private school I went to and the perfectly good state schools my friends went to was in non-education areas. Most of my school mates were daughters of high level bankers, foreign diplomats living in the area, large business directors & owners. There was a LOT of emphasis on "traditional, ladies" behaviours & occupations.
We had our own (rather small, unheated) swimming pool in the grounds. The school was housed in what had been a very large posh Victorian house. Gravelled driveway rather than tarmac/concrete. There were expectations we would have multiple uniforms e.g. everyone needed to have all 3 colours of the gingham dresses we wore in summer, and at least 2-3 of the enormously expensive winter uniform designed by the 6th form sewing class. Moved from soft straw hats in summer to hard boaters (mandatory, eye wateringly expensive, bloody uncomfortable). And the expectation that you would take extra classes like an instrument, private swimming coaching etc.
Meanwhile my friends at state school had just as good sports facilities (minus the tiny freezing swimming pool), more practical cheaper uniforms, still had the opportunity for (cheaper) private music lessons facilitated by the school, and just as good if not better education. However they didn't have etiquette and deportment lessons, and there'd been very little emphasis on things like sewing.
So going by my (limited) experiences, there was zero difference in practical education if not less at the private school due to other "skills" taking up the lesson times. So any tax on the fees there would be purely for the non-educational aspects of the school & curriculum.