Comment by Gormo
"Pretty quickly" may be an exaggeration there, given that 1740 was a good five generations after the founding of the Plymouth colony, and they were still famously conducting witch trials only fifty years earlier.
But it surely did happen -- IIRC, Adams and Jefferson were both noting in their correspondence how by the end of the 18th century most of the Puritan descendants had somehow become Unitarians.
Like I said, the halfway covenant was less than 2 generations after landing, and the character of Puritanism in America was totally different after that point.