Mother Goose rhymes were not always intended primarily for children. No one knows who the old woman with the unfortunate moniker was (or wasn't), but we do know the doggerel verse attributed to her surfaced sometime in the 17th century in England and France, and that the early versions were meant specifically to criticize or mock public figures.
Our versions are much more tame, yet they retain enough bite to stun even cynical modern readers, even children addicted to the overly-violent swill that passes for cartoons these days. Old men being thrown downstairs by the leg for shady bedroom infractions? A ladybug losing all her progeny to a ghastly fire? It's not exactly Disney, and it's not exactly the gentle fare we've come to associate with children's poetry.
Maybe we're making Mother Goose nursery rhymes sound worse than they actually are. At the same time, there's nothing wrong with kids' books being more edgy than Spot the Dog or Dick and Jane. The world isn't the quiet, calm place of 1950s suburban fantasy, and it's a bit of a disservice to present it as such to our children. Not that we need to terrify or horrify them, but just a small dose of pizzazz shouldn't be altogether abandoned.
These rhymes and short poems come in perfect measure. Some are merely lighthearted, others quite dark, some simply nonsense. While there are whole books showing the historical origins of the Mother Goose canon, you don't need that (often arcane) knowledge to enjoy them. And while few would try to defend any of them as high art, the older nursery rhymes do evidence a remarkably astute attention to meter and rhythm on the part of their composers.
The artwork for such books is often quite compelling as well, featuring colorful illustrations that present a somewhat shocking humorous mirror of the world as we know it. This is perhaps what nursery rhymes are best suited for, after all—showing us how things would be if chaos ruled, and making us very thankful it does not.