State churches are just guaranteed to be eviscerated over time, as seen both in the CofE and in the Norse churches.
The US is positively blessed to not have a state church, which by now would be an abomination.
This means that, to save itself, England must purge its government of churchly operations. It would probably do the CofE wonders to have to fend for itself. And after it had a reformation, directed by the conservatives of the Anglican communion, it might discover that people actually go to church to hear about God, not social policy.
And if it was out of government, there is no reason at all to invite Islam in to government.
Ahhh, but the U.S. DOES have state church(es), or at least state religion(s) — secular humanism, global warming, liberal ideology.