The original Q shows just how daft people are - that they don't realise that the point of education being funded through taxes is so it is accessible and free at point of access to all - that it's not a method of each paying for what we have personally consumed.
It's such a poorly thought through idea, because the natural conclusion is only those with children in state schools should pay and everyone should pay exactly what it costs to educate their own children.....seeming to be oblivious that very many couldn't afford to do this.
If you are fortunate to have the choice to fund private health or education for yourself, you pay your share of taxes towards the provision for everyone and accept that your good fortune to access an alternative has to be paid for on top. You accept that not everyone has this good fortune and if you want to feel some kind of justification for what is essentially an unfair system, you can feel pleased that you're not accessing and using up the state provision, leaving a bit more for others.......but certainly not to feel you deserve a refund of your taxes.
And regarding the impact of removing the special tax status of independent schools - yes, it will mean some close down and some parents can no longer afford the fees. There will be extra children in the state system, drawing on those limited resources.....but in all liklihood (and I do t have figures to support this) the government might save more through not giving tax breaks, than it costs to add those extra children. It would cause some disruption and issues in the shorter term in particular, but it would be workable. Why it doesn't happen though and is unlikely to, is because parties fear it would be politically damaging because it would be unpopular with influential chunks of the population.
Independnet schools will never welcome a removal of their special tax status ..... Of course not, but if it ever happens, it can hardly be seen as a huge surprise or impossible to justify can it?? Those schools might keep banging on about the public benefit they offer if bursaries and access to their facilities for the community, but essentially they are receiving huge subsidies which benefit the already well off and wealth is being distributed towards them. So if it ends, there won't be a good case for complaint and they won't get much sympathy from everyone else who uses the state system.