For a big-ticket movie, the science-fiction epic “Interstellar” is highly unusual. It cost a hefty $165 million budget to make, but is also wholly original—that is, not based on a comic book, TV show, or young-adult novel. Amid much hoopla, it opens across the country on Nov. 7, after two days of special showings in 250 theaters.

The last time a studio made a movie that cost so much and wasn’t part of a “franchise” was 2010’s “Inception.” Like “Interstellar,” it was directed by Christopher Nolan, one of the very few directors to whom Hollywood issues a virtual carte blanche—along with extreme veneration.

Mr. Nolan’s ability to combine box-office success with artistic ambition has given him an extraordinary amount of clout in the industry. Studios pay him as much as they do elite stars. Warner Bros. provides him with all the benefits of a studio deal with no strings attached. They indulge his personal passions—his love for traditional celluloid over digital technology, his fondness for IMAX big screens, his penchant for extreme secrecy. And they leave him alone, letting him go away and make his movies with little interference.

For a director to wield such power flies in the face of the current movie-business model, built upon superheroes, cartoon characters and wizards cycled in and out of multiplexes. Increasingly, studios occupy the driver’s seat on these massively expensive “event” films: Directors are hired hands. In recent decades, few besides Steven Spielberg and James Cameron have been entrusted with near-total control.

Mr. Nolan, 44 years old, is known for his well-regarded trio of “Batman” movies, which together grossed $2.5 billion at the global box office. Even though his latest picture has little prospect of spawning sequels, toys and theme-park attractions, everyone wants to work with him. “Interstellar” is being promoted with all the hype of the latest “Fast & Furious” or “X-Men,” from the immersive website created with Google to a surprise, debut appearance by Mr. Nolan at the Comic Con pop-culture convention, where the crowd of 6,000 went wild.