My own feeling is that in an age of soaring university costs, housing costs (ouch) and everyone having to put more into their pensions, private school education really does have to justify itself in terms of "more or less guaranteed" significantly increased lifetime earnings. Otherwise not worth it.
Because unless you are simply rolling in money, any money spent on private school fees is money that can't be spent on uni or helping your child start an investment fund/put down a deposit on a property.
If I was 35, living in the expensive southeast and had a load of student debt and my parents couldn't help me out with buying a property either, and the reason for this was "Well, we sent you to a private school.... and okay, sure, you didn't actually do any better in terms of exams/career than your friends who went to decent state schools, but you got a holistically well-rounded experience and lovely green fields and a nice orchestra and a wonderful drama club out of it...!"
... well, I'd feel a bit cheesed off, to be honest. And I'd be thinking that what would make me feel holistically well-rounded right now, would be if I could buy a house/flat and not have a millstone of debt round my neck.
Of course, if one is really rich and can easily pay for ALL these things for all your kids, then this is all immaterial.
I don't know many people like that, though. The only people I know in the UK who are using private schools right now, are doing so because they are in areas where there is a lot of pressure on school places and they only got offered terrible/very-far-away state school places. So they opted to go private until either a better SS place comes up or they move or their child goes on to the next stage of education (secondary/sixth form).