The songs that don't work for unaccompanied singing, are songs written with long breaks for instrumental parts. A cappella singers naturally extend notes or shorten rests to avoid "dead air," but some songs just don't seem to allow for such adjustments. I'd say it's mostly pop songs and songs with complicated rhythms that may not work for unaccompanied singing. I love "Chantilly Lace," but I can't figure out how to sing the song without accompaniment.