FACT: Recycling footage of "The Cage" in the episode "The Menagerie" was actually a last minute cover for a failed attempt on the part of Roddenberry to actually tie the Forbidden Planet narrative into the Star Trek backstory.
The original episode, which only made it to script stage, Kirk and Commodore Mendoza pursue Spock to a planet in the Altair system that was formerly the home of the Krell. Off-limits now for nearly a century, Spock was drawn to the rubble of Altair IV when he began studying the reports of the rescue ship, the C-57D, of a century before. The plan was ultimately scrapped on two accounts.
Gene Coon wanted Anne Francis to reprise her role as Altaria, but Francis declined. Coon briefly considered other bit-players from the film, but ultimately, the failure of MGM to grant the rights to use the footage from the original film (to have been used in Francis' or someone else's flashbacks) killed the project.
Rushing for a filler, Coon asked Roddenberry about using "The Cage", which Roddenberry had wanted to hold back as a 'film of the week' possibility. He relented, the adaptations were made, and the show went forward as we eventually saw on TV.