I've heard "Over The Rainbow" and other songs like Elvis' hit "I Can't Help Falling In Love With You" used as lullabies to put infants to bed on various occasions. They are being used for the same purpose as "Go Tell Aun't Rhody" going into tradition for traditional uses in the same way songs by Stephen Foster and Brahms did toward the same end.

And if the baby won't go to sleep, you keep pulling out songs, ANY songs, from the hat until they do, because what worked for Gartan Mothers did not work on this particular night. Nor, maybe, did songs written specifically to be "folk lullabies",like "Hobo's", "Prairie" or "Liverpool" which folkies find perfectly acceptable. If the song gets the intended job done, it becomes a tradition, if only a family tradition, and if a lot of folkies from the 'burbs turned to the music out of frustration from lack of traditions, the lullabye will still thrive anyplace, any time, any culture.

See, you had a tradition all the time, but you managed to sleep through it without realizing it!

Apply the same criteria to other tasks and see what other songs have passed into tradition.