Would I prefer to be unknown and unrewarded.
Would I prefer to be known and unrewarded?

The latter, presumably, but to rule out the third "Would I prefer to be known and rewarded" is to rule out common law and ethics. I repreat; why should composers not earn from their efforts as any other writer or artist?

You see you can't ring fence folk songs, and treat the writers differently to other types of music, just because of the way the material happens to be used - you could never decide where to bang in the posts. (Youd have to define Folk Music in law for a start - and the best of british the the one who tries)!

Law and ethics are as they are because they have been delveloped over time to bring fairness to the sharing of intellectual property, which happens to include folk songs, both ancient and modern.