Triple parallelism is a well-known rhetorical technique. (I'm not saying folk song writers knew about it -- I'm sure they didn't -- but it's known to be effective.) Abraham Lincoln was particularly fond of the technique. Take the Gettysburg Address, e.g.: "we can not dedicate -- we can not consecrate -- we can not hallow -- this ground." "that government of the people, by the people, for the people, shall not perish from the earth."

For that matter, the tupical meter of ballads is four feet then three feet. In a way, that in itself encourages triple parallelism.