@Goldenbear you seem to fixate on one very specific element of diversity (economic) to the exclusion of all others (race/ethnicity, cultural, gender, etc.). You are correct that most private schools are not ‘representative’ of broader society in that they don’t reflect the precise mix of society at large. Few state schools would meet that criteria though, as communities segregate themselves and therefore catchments will reflect that segregation.
you are incorrect however in your implication that all sectors of society are not represented in private schools. Schools will vary in extent of diversity- true for state as well as private - but the private school in my area is much more diverse by any metric than the state school we left.
Our state school was a village primary in an area of higher than average home prices - almost everyone was middle class or above, and it was 100% white native English speaker. It also had a lower than average level of SEN. Our private school on the other hand includes multiple children in care and refugees. All classes are represented to some extent, and it is a popular choice amongst trades and farmers in addition to teachers, doctors and lawyers as well as people who don’t seem to have to work at all for a living. There is far more racial diversity, and many are native second language speakers. We also have SEN at higher than average (about 2x national average and 3-4x more than the local state).
our school doesn’t precisely represent the community because it is more diverse than the community. The bit that is missing is the ‘can’t be fucked’ sector of society - all of the children at our school are there because they have adults in their lives that value education and prioritise their children. Being in a place where all children are valued is a sort of bubble, but one that I am happy to live in. I personally grew up in poverty, neglect and abuse and am quite happy to shelter my own children from that experience, not that I remember any of my middle class state school classmates having much to do with those of us on the wrong side of the economic divide.