To address the issue right away, movies are not completely absent from “Star Trek,” as they were actually regular occurrences on “Enterprise” and were resurrected for “Star Trek: Discovery.” On the former program, Capt. Archer (Scott Bakula) liked to hold regular screenings, partly as a pastime the crew could share, but also to expose the Vulcan T’Pol (Jolene Blalock) to human art and culture. She was particularly intrigued by James Whale’s “Frankenstein.” It’s implied, however, that the database of movies is limited, and the films they discuss are from Hollywood’s Golden Age. This will go into a theory about the fate of cinema in the “Star Trek” timeline that I shall explore below. 

Also, when the crew of the U.S.S. Discovery found themselves in a strained position, the ship’s commanders boosted morale by hosting an impromptu movie night in a cargo bay wherein everyone watched Buster Keaton’s “Sherlock, Jr.” But while the Discovery had access to the comedy classic, one might note that the Starfleet officers merely stood around or sat on storage boxes to watch the movie. There was no “screening room” setup. This was clearly not an activity that was regularly indulged in. Sometime between “Enterprise” (set in the 2150s) and “Discovery” (set in the 2250s), films fell out of vogue. 

On “Star Trek: Voyager,” officers regularly visited the holodeck to reenact a black-and-white sci-fi serial created in the 1950s. See the episode “Bride of Chaotica!” (January 27, 1999). It seems the general language and influence of cinema will remain in the human consciousness as far ahead as the 2370s when the show is set. But, one might note, that the officers don’t merely watch the sci-fi serial, preferring to perform in it. Which brings me to a theory: