Sigh, Andy, you are showing that you still haven't grasped it. It doesn't matter that some (a few) of the rich and powerful send their children to state schools. The majority don't. These people are not idiots.  They choose private education because it buys them something - some of what it buys them is a better academic standard, some of what it buys them is status, an education where they are taught that they are the elite, the ruling class, where they are taught all those little nuances that allow them to be prosper.  It's a divisive system where the common people's education is looked down upon even if can be just as good, where the old-boy network flourishes, and the same families, same crowd with the same outlook keep and grow their wealth and their power and pass it on from generation to generation.  You have to undo such a system before you have a chance of fixing the problems it creates. 

If this is your understanding, Martin, it shows how little you understand about private education, Martin!!  Yes, there are some who will send their little horrors to such schools for this reason, but many send them for other reasons.  For some it is the sports education; for others, its because they don't want to send their children to schools in the countries in which they work - if there are any that cater for ex-pat children anyway (when I was at school there were probably 1/4 of the student body in this situation and the same applied for many of the other 'local' independents like Marlborough, Radley and Stowe).  For some, it's because there simply isn't the room in the local state system, and they therefore scrimp and save to enable their children to get any education at all.

I'm afraid that you want to simplify the issue beyond all reality to make a false argument.