Gosh, Xenia it's good to have you back and see you've tempered some of your opinions during your break
I went to one of the best private schools in the country in the sixth form - the sort children are tutored from birth for. It was a brilliant school for someone like me who is academic, driven, tough and from a very secure family background.
I and many of my peers did well. Some are household names now. However, some had a miserable time - often the ones who had been tutored from birth - their parents were fixated on the name of the school rather than whether it was the right place for their child. A lot of them ended up in rehab or having breakdowns. One recently died aged 39, surrounded by drug paraphernalia in the million pound house his father bought for him. Many of the children never saw their parents because they were doing what Xenia considers every parents' duty working every hour of the day to pay the exorbitant fees. Or they very strained relationships with them because they weren't top of the class. I think they would rather have had some family life than attended such a school.
Although I've had a reasonably glittering career, I've come across plenty of contemporaries at Oxbridge and in my career who've done as well/better than me who went to bog-standard comps. If you are clever, driven and from a nurturing background you do not need a private school education to succeed.
Finally, in reply to the OP and to rebuff Xenia's suspicion that most privately educated people do climb back on the ladder, dh went to a posh prep school and as a result knows many people who went to nice-but-dim public schools. One has a terrible heroin addiction, most of the others are riddled with anxieties and inadequacies. Their parents paid for the perceived social cachet of these schools when their children would have certainly ended up happier and, I suspect, done just as well or better from a career pov if they'd gone to the local comp, where they wouldn't have wasted their lives worrying about who was going on whose shooting weekend in the Highland or who was going skiing with Prince William. Some state schools are dire, some private schools are dire. You always have to look beyond the label/the history/the prestige or lack of and decide if a particular school will suit a particular child.