There seem to be two different discussions/debates here. One is that some people simply can't afford private schools, however crappy their state options are. I live in horror of this fate, not least because we couldn't in fact afford two lots of secondary private fees. We can just afford two lots of prep fees - but only just.
If you are in this position, as the OP claims to be, then you have to think about it early - not leave it as late as the OP appears to have left it. The options are: scholarships; join the clergy or armed forces; or get a job at a private school, thus getting a discount on fees. Failing that, you have to move to an area where the state schools are ones that you would be happy (or relatively happy) for your DCs to attend.
To my mind, the fact that we can't afford secondary fees is not insurmountable. We have a fair while to make sure we can somehow get both children into private secondary schools by hook or by crook. I am not an 80s child for nothing: to my mind, if you want something enough, you will move mountains to make sure it happens. I want my children to be educated in independent schools from 5-18 more than I want anything for myself. Not because I want them to be in some way superior or to make friends with only "suitable" (ha, ha) children - but because I believe that their interests are best served by schools that don't follow the NC, don't do SATS, do bother with the arts, and so on, and so on. If it really comes to it and I can't afford it despite everything, then I shall take them out of school altogether and find tutors for the subjects that I can't teach them myself (namely anything scientific).
(I think this burble is probably aimed at the OP!)
So while there isn't a "choice" for some people, other people do have more choices about education than they like to think. It seems to me that some people are more comfortable with the idea that they can't afford it, rather than busting the proverbial gut to do something about it (not aimed at anyone on here - just a general observation).
That leads me on to the second, rather different discussion. And that is: if we agree that private schools really are not an option for many, many people - then what about those for whom it would be an option, if only it weren't against their principles? In a way, principled state-schoolers would be doing the Right Thing by opting for independent education, thereby freeing up a place at a good state school for a less well-off child.
Oh, I don't know. What do people do who really do live in areas with direly awful schools (like our local secondary), and who genuinely can't afford an alternative, even if they convert to the priesthood? What a horrible system it is.
PS UQD: that was just me being grumpy. Sheffield bugs me because it's such a terrible place for school-selection-by-income. When we tried to move to S11, we were priced out of the market by the fact that everything we looked at was in the Dobcroft/Silverdale catchment area, thus astronomically expensive. And we didn't even want the children to go to those schools!