Well, if you've ever tried to compose anything that rhymed, you've probably noticed that it's hard work. So here we have a bunch of kids trying to rhyme something with nurse. How many words rhyme with nurse? Not many.

purse
worse
disburse
disperse
curse
hearse
terse
verse

That's all I can think of. Now look at the list and see how many words can fit into a list of people (doctor - nurse - disburse? No.) Factor in the need for rhythm, and an alligator purse is just the ticket.