But, dave, you do not have to have experience of something as a customer to be able to administer it. In fact, as far as State education goes, it could be argued that the very experience makes many people singularly ill equipped to administer State education or indeed anything much else.
I simply don't understand the notion that only the State is able to properly provide some services (education and healthcare immediately spring to mind) when in fact quite the opposite is true. There is no doubt that private education is far superior to the State version. This is not entirely the State's fault; it's often because, having to take all-comers, many state schools are burdened with a high proportion of pupils who have no intention of learning and do their best - usually quite successfully and often with the collaboration of their parent(s)/significant other(s) - to scupper the education of the children that do want to learn. Private schools have no such problem as they quickly identify and deal with any miscreants.
This problem will persist and worsen in the UK as the number of "good" state schools gradually diminishes with government reducing the ways in which they can legitimately select their pupils. The end result of this is that decent jobs (including those in politics) will become more and more the preserve of those who have received a private education because they will be the only people educated to a decent enough level..