Xenia - you said that
"It's all pretty simple. Most women aren't bright enough or don't pick careers which are well paid enough to buy their children a good education so they make do with state schools. Women who can afford to pay fees tend to be pretty happy with the schools they choose.
If you can't afford it there is not much point in worrying about how much better many private schools are although you could look at what you might do to earn enough to pay fees, set up a business etc etc. "
Ignoring the obvious point that most women are not, unlike yourself single parents, and so whether they pick well-paying careers or choose to be SAHMs or go for low-paying but meaningful jobs etc etc, is either irrelevant or at best only a part of the picture re their financial situation, you seem to be hard of understanding today as you seem to have problems grasping the fact that were these same women as rich as Croesus, they would have no interest in sending their children to private schools.
I can honestly say, Xenia, that no amount of money you could pay me would persuade me to send my dcs private - and the idea that I would actually choose to pay myself for the 'privilege' is laughable.
For me, education encompasses moral and spiritual education as well as academic - whilst on academic grounds I agree a top private school can match a top grammar school (though I see no evidence it can do more than that), when it comes to the values I would like my children to learn, sending them private would work against all the moral lessons I wish them to learn. I don't want my dcs to learn that money gives one an entitlement to everything - much like the bankers etc now - and to believe that everything meaningful in life has a price put upon it.
Whilst I am sure that lots of people get a private education and thanks to a strong home environment, do end up as decent, morally upstanding individuals, I think it no accident that our current load of idiots in govt were all privately educated.
It is no accident that all my grammar-educated friends are left wing (one just selected for a safe Labour seat last week, actually!) - this reflects the values of meritocracy and equality of opportunity that run through the system and are central to it.
I am sure that you would hate those values, Xenia, much as I dislike yours, so it is indeed a good thing that there are schools for all sorts.