I'm not familiar with American children, though maybe I will be one day as I now have a Minnesotan grandson (but he's only one year old now). When you in the US were schoolboys, I mean this would be the 1950s, were you as objectionable as we must have been in the UK? I mean, I've forgotten most songs we had but one had a verse going like this:
Hey Jemima, look at your Uncle Mike, he's in the country, riding a motorbike
First he does a backfire, then he does a skid, now he's in the hospital, thinking about his grid!
And for poetry, we used to recite:
Hush little baby, hush quite a lot
Bad babies get rabies and have to be shot.
Or this one:
Poor little thing, got no feathers on its wing,
got no mummy, got no daddy -- break its bloody neck!
Were you like that in the US?