"I suppose the thing is religious people likely won't choose the non faith school, and atheists will likely choose the non faith school. "
?
You aren't listening, are you.
There are not 2 options here, faith/non-faith, religious/athiest. There is more than one faith! Unbelievable, I know.
So in your example, as a "faith" person you would choose the "faith" school. Only if it's a different faith, you can't go there can you. You'll have to go to the "non faith". Oh dear.
What if you, as a faith person, get into the "faith" school. It's not over-subscribed and you get in. Woohoo! And the faith is Paganism, or Exclusive Brethren, or even mainstream Muslim or Hindu. Are you happy then, as your children are at a "faith" school?
What about the fact that there are no athiest / secular state schools in the UK, so those people have no choice whatsoever.
What about the fact that people who are not fussed one way or the other end up having their children randomly indoctrinated in a religion, and which one it is, is down to chance?
It is a POOR SYSTEM.