So much of my childhood was spent jumping rope that the words and rhythms of the songs -- 50 years later -- still come readily to mind.
When I taught elementary school, I was surprised to find out that the children in my school no longer sang songs when they jumped rope. As the songs were always passed down from child to child, teaching them seems silly and almost defeats their purpose as a kid thing. Certainly the words were nothing particularly profound or important. As an adult I would prefer to have the rhythms of great poets come quickly to mind!
Still, I think the rhythms served their purpose. They kept us focused on the exercise. They helped establish the rhythms of language and they encouraged us to make up our own combinations of words and rhyme in a way that adult directed activities would never have done.
Maybe it was an urban thing, and rural children, without the numbers of neighborhood friends from which to draw, found other ways to use their time. Maybe children of today, too, have other rhythms they create in play.