Every high school kid knows Arthur Miller’s “The Crucible,” the allegorical play seemingly about the Salem witch trials but really fighting the chill of McCarthyism. In that play sits John Proctor, a righteous American farmer who finds his prior affair with a dangerous girl named Abigail makes him vulnerable to her lies, as used in service of those who will take him down.

Miller intended Proctor as a flawed hero, maybe a man not unlike himself. But the lively, moralistic new show starring Sadie Sink (“Stranger Things”) on Broadway undermines Miller’s 1953 view of the world by applying contemporary, anti-patriarchal thinking. The point of the mostly melodramatic play, set in a contemporary high school classroom in a small Georgia town, is right there in the title: “John Proctor is the Villain.”

Part of the problem, of course, is that once you understand that Sink’s complicated Georgia high school girl, Shelby Holcomb, is a version of Abigail, and that her seemingly supercool English teacher, Carter Smith (Gabriel Ebert), has similarities with Proctor, you know where the play is going. Miller was interested in complexity and ambiguity; playwright Kimberly Belflower is on more of a single-minded quest: to recalibrate the dominant view of a play so seeded in U.S. education curriculums and maybe even get a place alongside it in the future.