I also had mixed feelings about the grammar school I went to. Where I grew up there were eight such schools in a small area. Around 1000 kids per year were academically streamed and given (arguably) a more suitable education. I've thought about this for a long time, because although I benefited from such a system, my brother and sister (who attended the local comprehensive schools) were negatively affected and to a disproportionate level. There was very little aspiration in their schools, very little academic success and this had a knock on effect on their life choices. After a few decades to consider the matter I think I'm against selective streaming into separate buildings - though not against selective streaming within a school
The fact that you received a stellar education and a charitable one does not negate the net negative. At least in my mind. Individuals can thrive in a system which has an overall negative affect and I think that's what the Private education system does.
And I agree with you (in part). I have taught children from comprehensives and private schools - there is a difference which emerges around the age of about 11. It's subtle but it's there. Privately educated children do not treat you as an authority figure, they respect your authority (generally) but they see you as an equal, they talk to you respectfully but with themselves posited as a proto-adult. State school kids talk to you like you're an adult who should not be crossed. I have long considered why this is the case... because it leads to more confident and assertive adults by aged 18. The sort of people who might do well in politics, the arts and/or other people-focussed careers. I don't think it's intelligence, I've met some absolute dunce private school kids (now working in PR firms) and some very clever state school kids.
It's class size. It's adult attention in a non attention competitive environment. That's it. Plus there are plenty of additional buy ins in terms of activities/facilities. If you take away private schools and you plough that money into the State sector, then in an ideal world what you'd see is what happened to you, but for every child who comes from poverty.