it really does depend on the school. we moved to be near GParents, lovely local high school. In the 5 yrs it took for my eldest dc to be moving up the school went into special measures. GPs paid for dc to go to a local private school.
they had kids whose families were worse off than us (the school was particularly good for children with dyslexia and some families pulled out all the stops to send one child to it), some were on full scholarships, others were loaded .
One of my dc went to an event up in London and reported back in shock that one of the other teens on the trip had rung his dad in Saudi and asked for £1k for the weekend. same school, different worlds.
Mine are all adults now - the school friends they stayed in touch with, and are still friends, are all lovely, genuine, people, who all support each other. I have no idea whose parents are mega wealthy and whose are not. Having money, or not, doesn't make you a better or worse person. I came from a poor, WC, family exH came from a solid, comfortable, MC family. One of my siblings had a partner who was a millionaire - one of exH's siblings married a plumber....
The question is "which school is the right one for this DC, in this place and time?" it's not a theoretical question. You have to make the best choice you can, on the evidence you have, within your current resources. If the private school looks like the right one then go for it. One of mine had to be moved at it wasn't right for them. Be flexible. All we can do is the best we can.