Since a folk song had to start somewhere, it becomes a mystery as to whether it started
as a harmonized piece of music or an untrained melody suggesting chordal implications.
Most European-based music suggests harmony of some sort defined by chordal patterns that have survived in a specific tradition of music.

The unaccompanied ballad has its own merits but is by no means the definitive source.
Folk music is not classical music in that it tends to be a pastiche of varied influences and forms. The times the unaccompanied ballad sounds best is when the untrained musician leaves it alone and doesn't try to harmonize it without understanding the harmonic nature of the melody.

If folk music has a relevance today, then it requires a study of it historically and an interpretive input by contemporary standards. Without the latter, the performance of folk music is relegated to a slavish imitation of the past which is robbed of its true authenticity since it has been taken out of its historical time. Folk song scholarship is not just the unearthing of texts and their study but includes a musical timeline that can be identified.

There is something a bit oxymoronic about folk music scholarship. Folk music is a social music that defies putting it into a glass case or museum. It constantly changes. This is why a folk song has "variants".   A song may be sung one way on one side of town and different on the other side.

There is something to be said for an unaccompanied song but a case can be justly made for a "variant" that has a tasteful accompaniment which may give it a new dimension.

As in the study of logic, the notion that "it has always been done this way" is a kind of
artistic fallacy. It may not have been.

Antiquarians are generally on the losing side of history.