Blimey OP. You've been at this for days.
Education in the U.K. is a postcode lottery. Good for you if you have a good state option. Would you send your child to your local comp if there has been a recent stabbing? What about a grammar school - would you shun those too out of principle?
Basically, the decisions most of us make for our kids' education are driven by the specific range of local options. If there is a good comp and a 'meh' private school, most people would choose the comp - but if they had a school like Westminster within reach and a very bright child who got in, then they would probably not turn that down. Totally depends. Boarding school is a whole other ballgame again. We would not consider that, personally.
We have put 4 DC through independent schools from age 4. We ourselves come from countries were education was not even universal (DH) and absolutely shite (me). However, my husband has been very successful in business in the U.K. despite his origins. I haven't, but here we are, could be much worse.
What I have noticed in this country is the focus on 'manners' and 'soft skills' in the independent sector. When we visited the local state schools, none if the kids made eye contact when we entered the room or in corridors. It was like they were kind of skulking or shuffling around, smirking. That was the vibe. In the independent schools, they tend to look you in the eye, shake hands, open the door for you and hold a conversation without 'attitude.' Every morning and afternoon they have to shake hands and look the headteacher in the eye and say 'good morning / good afternoon.' Also, they stand when teachers enter the room and this kind of thing. There is no nonsense about not wearing the uniform, or not doing PE because of 'mental health' or a sore finger or whatever and excuses over homework not done or poor behaviour are just not tolerated.
Having said this, mine have attended very different independent secondary schools. One went to a top London Day School. It was very fast-paced and socially quite tough, but very diverse, ethnically and lots on bursaries (about 25% I think). I don't think he had the happiest time there socially, but he was happy being quite average there as he's quite laid back and not bothered about the academic competitiveness. In the end he got into Oxbridge, so all good. Second DS is dyslexic and academic performance 'spiky' and 'average' so he couldn't get into any London schools and had to travel quite far out. This school was supposed to be small and supportive, but turned out to be absolutely shite snd he would probably have received more support in a state school. I had to educate him myself, basically. The school was not worth the bricks it stood in. Anyway, he's got into uni to do 'his passion' but my god, that school was crap. The other two are in an all girls 'super-selective' and this school is fantastic overall. Few iffy, loon teachers but there always are.
Anyway, probably if we lived in the suburbs or outside London our kids might well have gone to the local comp and we'd never have known about selective schools or considered private schools. We're not even British. But actually, many (most?) pupils in London independents have at least one non-British parent. The schools are very international. World away from our educational experiences, but I'm glad they've had opportunities we never had. That's the whole point!