Balliol, of course you can't coach any child through the 11+. It's a competative thing - if 10% pass and 15% are being coached for it, then a third of them will fail. Whether or not the right third fail is moot.
And if you could, why on earth are you so in favour of grammar schools? If all (or most) children have enough intellect to pass, then why bother creaming off the ones that have been coached - better to send all to a comprehensive really.
I do feel a bit guilty that I can afford things that others can't (not just education), but I also believe in choice - of where to live, holidays to take, type of house & car, extra curricular things, as well as of schools.
All these things are only choices for those that can afford them (so polo lessons aren't an option for all, & neither is driving an aston martin), but unless we move to a communist society I don't see a way around that. Even in a truely communist society you still won't get equality of education for all children, as so much depends on the home environment.
As it is, private schools are a bit of a motivator to raise the standards of state schools so are arguably good in that respect.
The best way forward is to work to raise the standards of all schools, with the focus on the lowest ones as seems to be happening, though it has a long way to go.