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The children they educate
Indoctrinate.
That's a rather simplistic view.
I'm an atheist parent of a child who's being educated at a faith school. I see no indoctrination.
I'm not saying there is no indoctrination at all within any faith school, but then each school will vary. In the same way that not all public schools remove all sense of moral/ethical correctness in their pupils and instill supreme arrogance. And that not all state schools leave the thick kids at the back to eat crayons and never give them any form of support.
I don't think the general population would be willing to have an appreciable rise in council tax to facilitate this if implemented all of a sudden.
Faith schools are part funded (10%-25%) by the church/synagogue/etc that they are linked to. The children they educate would still need to go to a school so if this funding disappears the Government have to make up the difference or they have to find new schools in the same area (which generally there aren't).
Also, many of the faith schools are on land not owned by the local authority. There would be a huge real estate bill to buy it to run a non-faith school on the same site.
The government are dealing with this (slowly) in that any new faith school being built is capped at a maximum of 50% faith entry. I can see this slowly being increased over time to eventually separate faith and school. (See: https://en.wikipedia.org/wiki/The_50%25_Rule)
(Disclosure: My daughter goes to a faith school so I'm not entirely impartial, however as an atheist myself [my wife does the religion bit] I'm often surprised at what people seem to think goes on in a faith school. There is no creationism being taught.)