I had to duck out because of RL busy-ness, but am back too.
We have faith schools because of the history of education in this country. Before 1870 education was neither compulsory nor free. There were schools for those who could pay (some of which have survived as 'public', ie private schools). Nearly all of the schools set up for the children of the working class were set up by churches or Christian reformers. The Forster Education Act of 1870 maintained the existing provision and set up local school boards. So when education became universal there was already a patchwork of different types of school.
None of the subsequent reforms of the school system in this country has reformed the system wholesale -- not the reforms of 1944 which put in place the tertiary system of secondary modern/technical/grammar, nor comprehensivisation in the 60s, nor any since.
The result is that there is still a mix of publicly and privately funded provision; there are still schools set up and overseen by Christian denominations and other religions (Jewish schools for eg), there are still foundation/direct grant/academy schools, and there are still board/local authority schools.
No government has abolished faith schools for the same reasons that they have never reformed the system wholesale. Personally I think that all schools should be of one type -- that is run by the local authority and comprehensive. But how you unpick the faith schools part of the patchwork and leave the rest intact is a bit of a conundrum.
Should CofE schools all become academies (which can, under current legislation, be run by anybody, including a Church) or should they become old-fashioned 'community' (LA) schools? The only problem with the latter is that this govt won't let any schools 'convert' to being LA schools.
The problem is far more complex than simple rhetoric about 'faith schools should be abolished' can allow.