The more I think about it, the more I think we have been using the wrong word for the thing that is disappearing from American versions of British songs. We don't really mean "supernatural", do we? God and the Bible are supernatural, yet they show no signs of disappearing from American songs. Wouldn't it be more precise to say that the elvish elements are disappearing?   

As Janie has well stated, folk songs do "change to reflect the meanings and values of whoever the current 'folk' are" and therefore "it is not surprising that a good bit of the magical element has gone from the American derivatives of the old ballads".
God and the Bible are important to many of "the folk"; elvish knights much less so.

So could we say God is here to stay, but Elvish has left the building?

Kent