While I agree with your first point, I am not so sure I agree with your second. It is well known that Madison, the primary author of the Constitution, believed that the church was not needed to support civil society:
It was the Universal opinion of the Century preceding the last, that Civil Government could not stand without the prop of a religious establishment; and that the Christian religion itself, would perish if not supported by the legal provision for its clergy. The experience of Virginia conspiciously corroboates the disproof of both opinions. The Civil Government, tho' bereft of everything like an associated hierarchy, possesses the requisite stability and performs its functions with complete success; whilst the number, the industry, and the morality of the priesthood, and the devotion of the people have been manifestly increased by the TOTAL SEPARATION OF THE CHURCH FROM THE STATE. [James Madison, as quoted in Robert L. Maddox: Separation of Church and State; Guarantor of Religious Freeedom]
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