Hume, an agnostic if not an atheist, takes the position that religion is not a public good but its opposite — a public bad — and that government intervention will avert the pervasive negative externality of religious controversy, which clergy create and that threatens public safety.
The strongest argument for socialized medicine is the strongest argument for socialized religion, that government provision seems to reduce enthusiasm for and consumption of such things. Western Europe seems to have hit on the clever solution of loving both religion and medicine to death. Should we consider loving other cranks to death?
Imagine bureaus of palm reading, UFOS, conspiracy theories, etc. In a few decades they might be run by out-of-date boring bureaucrats following stacks of official protocols. If the best devotees were distracted seeking promotions in the ossified agency, they might inspire less public enthusiasm.
From an evolutionary standpoint an increase in diversity and competition caused by freedom of religion inevitably leads to selection of ever more compelling and virulent memesets (7th Day Adventists, Scientology etc). But by creating a benevolent state monopoly of the C of E the state has repressed diversity and hence the fitness of religion.
Certainly government endorsement immediately makes everything much more boring and unattractive (apparently use of cannabis actually decreased when it was relegated to a class C drug).