Bertrand to an extent the church want to have its cake and eat it.
A few years ago the head of the Oxford Diocesan Board of Education made a big pronouncement about church schools getting 'back to their roots' in serving the local communities. He suggested that they should change admission policites in order to admit local disadvantaged children rather that the 'pray or pay' middle classes who fill the pews on a Sunday as a way of avoiding the local comp.
It's a great idea. Sadly, it's a bit like my champagne socialist friend who goes on and on about how she only believes in state school education after spending an extra £50k on a house in order to get her child into the 'naicest' primary (with the lowest levels of FSM in the borogun).
Unfortunately, admission criteria for VA and academy faith schools are set by the governing board of the school. These boards are made up, in no small part, by local clergy, who have their own 'targets' set by the Diocese of how much 'collection' (for want of a better word) money they need to return each year.
When someone once remarked to our vicar that the church was very full of young families - bucking national trands - she remarked along the lines that it's amazing what effect having an oversubscribed outstanding local church school can have.
Removing faith admissions criteria will cause church attendance to drop - particularly in areas where the church schools significantly outperform other local schools. While the church may make lofty and noble statements about serving local communities, they have little financial desire to change the status quo.
I don't have the answer - I'm not clever enough for that. I wish that general state education was better for all.