Please don't for a minute think you are paying money to a charity. You are paying to a business with slick marketing and PR who sell themselves as a 'luxury good' which means they should be paying VAT.
Do you think most private school parents pick the school because of its charitable endeavours? I highly doubt it.
I picked our school because it was academically selective and has great sports facilities. While it's commendable that 10% of pupils are on bursaries, it didn't make any difference to our decision. Not being heartless but it was the case.
I have two friends who are senior management at private schools. One of their schools is barely solvent, particularly after pension liabilities. Not all prIvate schools are swimming with money. I'd also be amazed if the charitable status financial benefit cost the state more than paying for a state education for those pupils. Including the cost of building more schools to accommodate them, plus some teachers would face a drop in salary.
I achieved higher A levels than my privately-educated husband. It was also an advantage being a woman from a state school when it came to getting a job in investment banking as they were desperate to be more diverse.
I can't say I was bothered about private schools, as a concept or their charitable status. If people want to pay because they perceive it's worth the money, whether justifiably or not, that's up to them.