That I agree with...tho the Puritans sure tried.
Yes, the Puritans and some other groups did create their own little theocracies within the colonies and the new states. And the Founders, while they would not allow this in the federal government saw it as an unalienable right for the Puritans and other groups to form the society they wished to have. That is a concept we need to relearn.
History has worked out to show that with power of human freedom and unalienable rights protected for the first time in human history, every one of those little theocracies eventually peacefully dissolved and went away. By choice, not by decree.
Freedom won out over theocracy and no national theocracy has ever even threatened to form. Even strict Mormonism in Utah has given away to more tolerance and inclusiveness. Whenever unalienable rights are understood, recognized, and protected, humankind generally manages to arrive at a better place. We only get ourselves in trouble when we violate those rights in favor of different selfish and/or altruistic motives.
Actually they saw it as a horribly failed experiment and structured the federal government so it could NOT happen again.
Sorry, but it continued some time after the Constitution was ratified and the federal government did nothing to interfere with it. If I'm remembering the history right, I believe the last Puritan theocracy dissolved in 1799.