Though not essential, the value of rhyme is the same as the value of form. Form is the opposite of chaos (or random form and formlessness). In the creative arts, form provides a dimension in which creativity can be focussed, and therefore recognized and appreciated. Obviously, a painting of a sunset can never have the beauty of an actual sunset. But the opposite applies. Something that happens accidentally can never have the attraction of something which an individual has worked to create. Hope this doesn't sound too pompous. But the question touches on some interesting fundamental matters concerning things which distinguish aesthetics from mechanics.
This applies as much in a traditional song as in a Shakespear play.