Academic explanation for rhyming fillers with irrelevant meaning in doggerel
Regarding "The point won't hold after translation", maybe the words in this poem are relevant:

See you later, alligator!

After while, crocodile!

In an hour, sunflower!

Maybe two, kangaroo!

Gotta go, buffalo!

Adios, hippos!

Chow, chow, brown cow!

See you soon, baboon!

Adieu, cockatoo!

Better swish, jellyfish.

Chop chop, lollipop.

Gotta run, skeleton!

Bye-bye, butterfly!

Better shake, rattle snake.

Our school day now ends.

So, good-bye, good friends!