In reply to Pip Radish, are we not back to the question of whether the singer values the song, is committed to it? Without making the performance into a melodrama, it should still be possible to convey the tension in a repetitious song like 'Hangman, stay your hand' or 'Lucy Wan' -- if the singer believes in it!
I've been in clubs where such songs have been included in a performer's programme for the seemingly sole purpose of encouraging audience participation, at the expense of the central narrative. But if the principal purpose is to have the audience make a noise, then surely there are plenty other songs which would do the business -- 'The Twelve Days of Christmas', 'One Man Went to Mow' etc.
Try thinking back to when you were wee -- even when a child is more than familiar with a fairy tale like 'The Three Billy Goats Gruff', there is never any urging of the adult reading the story to cut out the unnecessary repetitions and get to the point (although that may also have something to do with prolonging bedtime!).
Bottom line -- trust in the power of a good story.