I have never met a parent who felt entitled to 'free', not least because 'free' is not actually free as the majority pay taxes. Nor have I come across parents who pay being belittled. Envied, yes.
Like the NHS, state education is free at the point of use. As a mostly 93% parent, I was not entitled myself. Neither do I belittle parents who choose private. My DD went private for sixth form. It was a choice I felt privileged to make, not only because I could easily afford it but also because I live in a country where such a choice is possible (for some).
Citizens cannot reasonably be held responsible for the deficit. Numerous factors created it: governments' failure to achieve economic growth since 2008; the ever-expanding expectations of the NHS; the COVID furlough scheme; debt interest; the economic impact of Brexit.
Neither is it the case that 93% parents take costs for granted. State parents are not provided with an itemised invoice every term, unlike independent parents. There is no reason for them to have awareness of costs.
The case you have outlined in summary is that you have made a choice without thinking it fully through or reading the small print. Now you are seeing pitfalls and you don't like them. Once again, you have a choice: pay the £750 or move your DC to the state sector.
Typo