The Academy of Motion Picture Arts and Sciences was wise to abandon its notion of a “popular picture” award for Sunday’s Oscars, but if organizers wanted a hot new category they might have considered “best spitting image.”

Never before have so many acclaimed actors sought to capture not only the style and voice of a real-life character, but also the physical appearance. It goes far beyond makeup—for which there has been an Oscar since 1981—and involves advanced prosthetics and orthodontics, resulting in on-screen images that...