It wouldn't be the first time a Trek episode has repurposed old movie footage. The historical scenes the Guardian of Forever showed in "City on the Edge" were from Paramount movies. The establishing shots of New York may have been as well. And a number of episodes recycled documentary or news footage, e.g. the Air Force Base footage in "Tomorrow is Yesterday," the NASA footage in "Assignment: Earth," and some of the whale footage in
The Voyage Home. Oh, and the first half or so of the
Enterprise main titles.
In TAS: "One of Our Planets is Missing," stock footage from Filmation's contemporaneous series
Lassie's Rescue Rangers is used in a video montage representing life on Earth, in order to convince the cloud creature that the planets it consumes contain sentient life.
Come to think of it, I'm surprised TOS didn't use more stock footage from old movies, considering that that was a pretty standard way to save money on TV.
The Twilight Zone made heavy use of the spaceship footage from
Forbidden Planet. The entirety of
The Time Tunnel was built around reusing stock footage from historical epics.
Battlestar Galactica used stock footage from
Silent Running to represent the fleet's agricultural ships, and
Galactica 1980 matted Cylon Raiders and blaster fire onto footage from
Earthquake to represent a simulated Cylon attack on Los Angeles.
The Incredible Hulk's first season had no fewer than three episodes (a quarter of the season) written around stock footage from Universal movies (
Earthquake again,
Airport '75, and Spielberg's directorial debut
Duel).
MacGyver's first season had episodes built around stock footage from
The Naked Jungle and
The Italian Job.
So you'd think a budget-conscious show like TOS would've saved some bucks by writing episodes around stock effects footage from old sci-fi movies. Then again, I guess the question is, what color SF movies were there in
Paramount's library at the time?
When Worlds Collide could perhaps have worked. Some of the spaceship and station footage from
Conquest of Space could've worked.
Robinson Crusoe on Mars and
Crack in the World could possibly have been useful too. Not sure about
War of the Worlds, which might've been too recognizably Earth-based. And
Barbarella's depictions of space and alien worlds were too stylized. So it's not a very large list of candidates, but it's enough to be of some use. And they could always have used historical-epic footage
Time Tunnel-style in parallel-Earth episodes.