Private school pupils make up much more than the 7% they represent of children. The private schools obviously do something right and most parents who pay are happy to do so believing they do their child good. If you don't think so don't pay. If both types of parents are happy that's great but the statistics speak for themselves, private school pupils made up 30% of Olympian I think, may be more, they are 80%+ of judges, they are about half the cabinet I think, and go through just about any profsesion except left wing local authority and you will see those who succeed have massively increased chances if at private school. Even if you take UK island owners (my category) we seem to have been to private schools - Ben Fogle, Branson etc.
If parents don't want to pay, don't. It's entirely up to you. If state school parents are genuinely puzzled as to why people pay (and I suppose just about I might have hda for my children the choices of places like Henrietta Barnet, Watford Grammar (which is comp not grammar), QE etc which are not bad state schools why do people pay for schools like North London Collegiate? First of all i wanted them in single sex schools from gae 4 - rather hard to achieve in the state sector.
Secondly wanted them educated in classes with only very clever children with 120 IQ = from age 5 - again hard in the state sector.
Music is very important to me - 3 of them won music scholarships and it tends to be better in the private schools.
Accent - not crucial and I am not that impressed how most teenagers speak in all sectors but perhaps marginally better in fee paying schools.
Ambience - nice to go to a school with lakes and parents' choirs and parents with whom I have a lot in common.
However none of those things matter as much for me as the fact everyone is very clever and I am buying a peer group who will go to good universities, 25% Oxbridge or whatever, very high expectations of careers at schools, feminism, most children getting mostly A or A*. There will be other reasons too - I have quite sporty children and that can be better at private schools too. Riding and lacrosse not impossible to do at state schools but less likely and were/are the passion of the girls - one now doing it for England, just chosen - congratulations her.
However 50% of children at the best universities went to state schools. The City has a lot of successful state school people and it's certainly not worth parents bashing themselves over the head if you are a woman who made such a poor career choice you cannot afford to pay fees. There are plenty of ways to skin a cat. And indeed your aims may be opposite to mine - you may want the children to have a particular local accent. You may want it to go into work similar to what your family does as the lower end. You may think there is nothing worse than church choral singing in parts and want tambourines and guitars. You might think competitive sport is a sin and competition the work of the devil.