Ah, the Puritan thesis (as outlined by historian Edmund S. Morgan in The Puritan Dilemma) rears its head again! But it really can't explain this specific phenomena outside of New England, as others have pointed out.

"The culture(s) of the British Isles did not cross the waters intact. In New World protestantism, the supernatural and magic were (are) nearly always regarded as the work of the Devil, that big Bad-Ass guy trying to trip you up. And the Devil is nearly always viewed as a trickster. And if you lose to the Devil, it's your own damn fault for not being 'good.'"

Perusing Ozark Magic and Folklore by Vance Randolph (among other sources) should make it fairly clear that British-descended settlers in the New World were not at all unfamiliar with magic and witchcraft (for lack of better terms) and were not always adverse to making use of it in their day-to-day lives.

So, admittedly, I too don't really have an explanation for the loss of the supernatural in Anglo-American folksong.