Thats more than simple correlation. Having kids when you are in middle age might have been known as physically difficult, especially for the mother. We've made huge leaps in medicine to trivialize child birth but for most of human existence, it was a game of dice, to some degree it still is, where mother and/or child could perish.

Maybe younger women cope better with the physical stresses of pregnancy? Nature seems to think so.

Not really. That's when they start having sex. So you end up having kids whether you like it or not.