The variety of banana (Gros Michel) that was commonplace when the "slip on a banana peel" comedic device was invented was a different breed than the one that is commonplace today (Cavendish.) The Gros Michel peel was reportedly very slippery.
as an addendum to that, the reason you don't see Gros Michel today is because "Panama disease" (a wilt fungus) wiped out most of the plantations in South America/Africa. You can still find Gros Michels in Thailand today. Someone should write myth busters, maybe they could import a gros michel to test it.