A variation of this would be, in the case of Bob Dylan, making tunes for those songs of his for which either only the lyrics were available or only existed on obscure bootlegs. I made a tune for The Ballad of Donald White. Many years later I heard the Blind Boy Grunt rendition......sorry Bob but Tramps and Hawkers doesn't really fit the song so I'll stick with my tune.
"Hallelujah"? I'll stick with Leonard's original. Most other renditions I've heard are boring.
On the other hand,"Love will tear us apart" from June Tabor and the Oysters....Wow!!
Another twist is when you're a songwriter yourself and you end up writing 3 versions of the same story 'cos you're not 100% convinced with each version!