It might sound daft but what is the purpose? A lot of traditional stories and children's stories tend to have a dual purpose. E.g. entertainment but also moral instruction or imparting knowledge or cultural traditions. However, some of the songs and rhymes from nursery don't seem to fit in with that. Do they serve any kind of linguistic or educational purpose then? Are they purely for fun?
The song that set off the train off thought was one I came across today that hadn't crossed my mind for years and years:
I hear thunder, I hear thunder,
Hark don't you, hark don't you?
Pitter patter raindrops, pitter patter raindrops,
I'm wet through, so are you.