The OP makes an entirely fair point. And apart from the injustice of taking taxpayers' money but saying 'you and you and you can't come into our exclusive club', it's not very Christian. Or good for the Church - the more children who are exposed to Christian teachings, the better in their eyes, surely?
I went to a CofE middle school - back in those days they were just local schools that took anybody in the catchment. And my senior school, although not a Church school, had Assembly every day and a Christian ethos. I'm very glad - it taught me an awful lot about the religion that has shaped our country and the whole of Europe (and the New World, given it was Christian Empires that went out and conquered it).
It gave me some great music, philosophy, some fantastic stories (I mean that in its real sense, not as a slur) and the ability to understand much of art, literature and music. A good grounding in the CofE really helps you get more from the average art gallery. Oh, and no doubt that's why I took religious studies O-level and got an A. ;-)
Seriously, evangelical Christians are fond of asking WWJD - well, if you've read the Gospels, it's clear he wouldn't be setting up exclusive clubs and saying 'you can't come in', especially when the people being excluded are children. 'Suffer the little children to come unto me'.