If we're talking about "tradition" per se, singability is obviously a requirement but it isn't the whole story.

"Napoleon's Farewell to Paris," for example, is "singable" in the sense that some few singers actually memorized and sang it. But its place in tradition, in contrast with that of "Barbara Allen" and the other usual suspects, was - so far as we can tell - minimal.

One feels that for most singers, "N's F to P" and its like were quite unsingable, and thus only peripheral to "tradition" in general, no matter how those who did sing them learned and (perhaps) passed them on.