'Be a Clown' with Fred Astaire?

It's been noticed that the final "Be a Clown" is similar to "Make them Laugh" in Singing in the Rain. But there is also a similarity with Fred and Judy's routine "A Couple of Swells" in Easter Parade. Both routines parity vaudeville with very loose dirty clothing. And both have a joke as the performers repeatedly prepare to exit to the audience's left. One was with Judy and Gene and the other was with Judy and Fred. And they were released within a month of each other! Judy was sure busy. Since "Be a Clown" seemed tacked on, I suspect that, although written for "The Pirate", it was added as an inside joke copying "A Couple of Swells",