It was NOT Arthur's idea to turn Gypsy's memoir into a musical.
It was David Merrick's idea. He read the excerpt of Gypsy's autobiography in Harper's magazine shortly before publication. The book was an instant New York Times bestseller, and Jerome Robbins became interested, seeing Gypsy's story as a way to tell the story of how vaudeville degenerated into burlesque and how Gypsy became a star turning it into a sort of art form.
Merrick and Robbins went to Arthur, who said he had no interest in writing a musical about a stripper and even less interest in providing a book to a Jerry Robbins cavalcade of cheap vaudeville and tacky burlesque numbers.
What WAS Arthur's idea--and it was a brilliant one--was to make the musical about Rose instead of Gypsy, so it would be a mother-daughter drama and not just another showbiz saga.
What followed were two years of arguments between Arthur and Jerry about the book scenes versus the vaudeville numbers. On West Side, Jerry had won when it came to the dances. On Gypsy, Arthur won, but Jerry still got his Jerome Robbins box.