The separation of Church and State has failed catastrophically:
Same problem as anarcho capitalism. The vacuum is apt to be filled. And today it is filled with an official government belief system that daily becomes more extreme, and is enforced more coercively.
In retrospect it is clear that in England the demand to disestablish the Anglican Church came from a competing religion, then called Evangelism, descended from Puritanism, which was already most of the way to becoming the state religion of England though it continually changed its name in the process.
The history of official religion in the US is more complex. When the United States was many separate states with a common defense and a common foreign policy, back when people said “The United States are” rather than “The United States is” there was absolutely no separation of Church and State, for each state had its own state religion, and the seminary of the state religion of Massachusetts, charged with promoting and enforcing the state religion, was Harvard.
After the English restoration the religion of New England became aggressive, political, this worldly, and bent on conquest and domination. They forever resented the English restoration which had disempowered them and purged them from lucrative positions in the Church of England and in the English government. Whig history began as their plan for reconquering England and the world.
The state Church of Massachusetts was state church of New England, and New England set up its Rome, its Papacy, in Massachusetts. The civil war and the Mormon war was New England conquering America — and then, following the civil war, denied it was a religious institution and proceeded to apply the doctrine of “separation of Church and state” as a very thin coat of white wash over the state religion of Massachusetts being enforced on everyone in America. And after World War II, everyone in the world, except those protected by nuclear weapons, Russia and China. There is a direct correlation between one’s alma mater’s proximity to the Boston–NYC–DC corridor and the height of one’s position in the government and ruling class of one’s country. Outside of Russia and China the only substantial resistance comes from Muslims.