One is that 'aspiration' is all very well but to imagine it is this - and not the fact that there are at least five people unemployed for every vacancy in Britain - that is the problem in the inner-cities just isn't engaging with the real issues that young people have to deal with.
The other is that (again) even if one accepts that 'social mobility' is the goal of the school system, these are unlikely to improve it. Say what you like about faith schools - politicians who praise them are quite literally willing to practice what they preach, in that they will send their children to them. But how many do you imagine would have their children in one of these institutions? I don't think the point requires explanation beyond this observation.