I was a teacher in a Catholic school in London for seven years. I can assure you from my experience in that part of London that parents' perceptions of schools bore little relation to what actually went on in them. The faith side of things tends to blind a certain kind of receptive mind to criticism. It made things very difficult for the schools that were perceived, usually unjustly, as not as good. Wholesale cheating went on with teachers and parents conniving in getting children's assessments adjusted, often downwards, to get them into the school of their choice, the intake quotas being thereby circumvented. So the faith schools got a better quality intake and would be able to claim, dishonestly of course, that the better results they got had something to do with the faith ethos. If that's the system you want to defend, I'm parting company with you.