I feel pretty strongly that tunes/melodies include implied chords (harmonic structure) whether or not any such "arrangements" were ever written, and whether or not instrumental accompaniment (or even additonal vocals) is present for a given rendition. That's just the way I hear music.

It might be argued that my sense of musicality is influenced by the fact that I play guitar, but I didn't take up the playng of that very "chordal" instrument until I was a teenager. I had been singing harmonies for many years before then, and the sense of finding a "correct" or fitting harmony definitely implies a simple chord structure.

One pedantic argument that really annoys me is that sea shanties could never have been sung otherwise than in unison. First of all, no recordings exist that could possibly support or refute this ridiculous assertion. Secondly, my observation of general group singing among living people is that some folks are incapable of singing in usision with others. I can't imagine that a group of sailors would not include a member of two singing an expressive but dissonant countermelody, and several others improviding some sort of more cenventional harmony, if only because their voices couldn't reach the notes required to sing in true unison.