I think it's important to distinguish between how the songs were performed when collected and how they were performed when there had been a "living" tradition of singing folksongs (accompanied or unaccompanied) or playing folk tunes (to accompany dancing or for any other purpose). Sometimes I've read about how songs were collected from people who were considered "old-fashioned" for singing the songs and they were no longer performed at weddings, gatherings, etc., and there was no interest in preserving them in their communities. It's typical of collecting that people start taking an interest in a thing when it's already disappearing.

I think it's reasonable to suppose that in most places, folksongs were accompanied, if instruments were present and people knew how to play them. There may well have been exceptions where certain kinds of songs were never accompanied.

I also think the term "folksong" or "folk music" tends to lump too many different kinds of music together and the term "World Music" is even worse in this respect.

I recently bought a copy of Johann Gottfried Herder's
_Stimmen der Voelker in Liedern: Volkslieder_ (_Voices of the Peoples in Songs: Folksongs_) --- a very early collection of folksongs (1778/79). In the introduction, it says that the first volume wasn't popular with the critics, because (to paraphrase) they weren't slick enough. In the second volume, he made more changes to the songs in order to make them fit in with the taste of the time. However, it wasn't popular, either, and the real enthusiasm for folksong in Germany started a generation later with Clemens Brentano and Achim von Arnim's _Des Knaben Wunderhorn_ (_The Boy's Magic Horn_). Funny how little has changed since then.