The stereotype doesn't come completely out of nowhere though - Cormac McCarthy: "If there is an occupational hazard to writing, it's drinking."[1]. Of course, he did some of his best work after quitting drinking, so it's definitely not true that you need to be a drinker to be a great writer.

[1] https://www.nytimes.com/1992/04/19/magazine/cormac-mccarthy-...