Yes, it really should, but I don't think of this as a major issue facing England or the UK, especially since the ensuing loss of state support would probably be a disaster for a lot of the country's architectural and musical heritage.
I fail to see why churches of cultural importance can’t be made into museums, landmarks, or repurposed into social centers for the community they previously served.
They can be. Will they be? I'm not sure I trust Britain's current political culture to do so, but I'd love to be wrong about that if a UK poster would like to correct me.