It's exactly what a PP said yesterday:
Part of education ( some would say a very important part) is meeting people from different backgrounds. The broadest intake is in State Schools. In some areas Secondary catchments are sorted to include children from as wide an economic background as possible. So where I live historically the children come from very poor inner city Primaries and also Primaries in rich areas.
The advantage to both sets of children is palpable. They get to see a life they have not themselves experienced before. Many well paid professional jobs require a knowledge of and insight into the least wealthy eg GPs, Barristers, Teachers, etc.
To me, this translates as thinking that everyone will hang out together and understand the difficulties of some people's lives. I just don't think that actually happens in reality.
As an illustration, one private school we looked at (big name public school) it was only when I asked a question about bursaries that one girl said she was there on a 100% bursary and the other girls in her year in her boarding house had no idea that she was on that despite having lived together for 4 years at that point. Kids don't really discuss that kind of thing.
At DD's comp, there are a number of parents who are household names, there's even a couple of members of the House of Lords. I only know because I recognise the names on the WAGs or because people offer to do sessions for the careers guidance workshops. DD had zero clue that those children had well-known parents.
Agree with you that private schools are not the domain of the posh even in top name schools - although the VAT is going to drive it that way. And a huge number of private schools are not catering for the 'elite' at all, but for SEN or parents who value education and can just about manage the day-school fees for no-frills but smaller classes, better behaviour etc.