I think that to classify the verse above as merely a children's playground rhyme is to ignore a whole political can of worms.

Charlie Chaplin was vilified during the First World War and long after by the jingoistic bigots who considered it the duty of every able bodied Englishman to sacrifice himself in the trenches.

Chaplin, far from being able bodied, was in fact declared medically unfit for service but this mattered not a whit to the middle class nonentities who were filled with resentment at seeing a poor boy make good in Hollywood after forsaking the shores of a country which had treated his family abominably.

The verse above is an expression of this resentment. It is not something which I would particularly want to sing myself, although it is admittedly cleverly written.

Then again, it is part of folklore and history, , along with whaling songs, and blues songs celebrating male aggression to women, so maybe it should be perpetuated ...