It's not as simple as that, Dick - it's not always the older versions that retain the supernatural elements, and there are 20th century-collected variants complete with elfin knights and magic fiddles. Bear in mind that the collected versions of any ballad represent only a snapshot anyway. The earliest known 'Demon Lover' (a broadside including no demon as such) is from 1657, but there's plenty of reason to suspect that the ballad had been around for some time before that. The original form of any ballad is a matter for conjecture.

Having said that, you can detect a general trend towards rationalism and, if the disappearance of the supernatural in American versions is indeed demonstrable, I'd guess it's because some of the ballads were enjoying a vigorous existence there, a hundred or more years beyond most of the versions at Child's disposal.