The same circular arguments ad infinitum…..
Governments can charge VAT on what they like. A private education is not a human right.
Private schools close and new ones open, and sometimes the private school population goes up a bit and sometimes down a bit. Mostly this is just a response to economic cycles.
It is not altruistic or good parenting to choose private, any more than it is to choose state. And, yes, parents can and will (rightly) help their children in many ways, not just schools. Middle class people s’ children will always be at an advantage.
Will it raise revenue? Probably. Will it raise significant revenue? Probably not.
But, like high rates of stamp duty, which is a truly stupid and iniquitous tax (it is basically a tax on divorce and mobility), I doubt anyone will reverse it any time soon.