The very word "broomstick" has for centuries been associated with female masturbation. Single older women that weren't nuns were watched closely for signs of witchcraft. One powerful piece of evidence was masturbating with a dildo, often a broomstick. From there, it was an easy thing to confuse the naive by describing a witch as "riding her broomstick at midnight". Once witchcraft was determined to be harmless and tales of witches only used to entertain children, the flying-broomstick image remained, while the more adult (and more factual) image was never illustrated.
Sexuality is so repressed in Disney Inc., I'm surprised that they haven't inadvertently titled a movie, "The Cock and the Pussy".