If not for the outbreak of COVID-19, the wildly successful Broadway musical Hamilton would embark on its fourth tour this fall. Instead—to the delight of fans and penny-pinching show-goers—a planned film version, featuring the original cast members, will begin streaming this week on Disney+, over a year ahead of its original theater release date. What was once available only with access to an urban center and extra cash is now coming to a screen near you.

Hamilton’s screen debut ...