I remember MacGyver having clip shows at least once a season. It was a common practice in action shows. Later series like Showtime's Outer Limits and Stargate SG-1 had annual clip shows built into their budgets from the start -- even though Outer Limits was an anthology series, so it was bizarre to see them try to retroactively lump multiple unrelated stories together in a shared continuity (although there was at least one season where they set it up from the start, using a recurring tech/robotics company in multiple episodes). The fourth season of the syndicated The Adventures of Superboy actually had two consecutive clip episodes. Hercules: The Legendary Journeys and Xena: Warrior Princess had fun with their obligatory annual clip shows, doing goofy frame stories like having the casts play caricatures of the show's production staff.
Technically, Star Trek: "The Menagerie" is a clip show; it's just built around clips from an unaired episode. Gilligan's Island's season 1 Christmas episode did much the same with footage from its unaired pilot.
Technically, but surely only to get episode count and series production cost under control by using footage designed solely to convince studio executives to commission a full series? That's the one difference I'm seeing in this. "Star Trek" was one of the most expensive shows to make at the time and it likely wasn't cheap to film Gilligan and the rest on location in Hawaii either (as the greenlit, official series never went back there but instead built a fake lagoon that had not-quite-tropical water in it). I'm curious on the Xmas episode to see how the pilot clips were used as there were some different castaways (removed/retooled for what would become the iconic group.)
The other shows' clip shows were just using repeat fodder to fill out time for episodes' lacking content that couldn't be padded out, or to make up for lost time, budget crunches, like what you said about incorporating a clip show in to the season (thus allowing money and time to be appropriated and applied better, especially if script rewrites were needed), or other behind-the-scenes issues. It does sound like Xena had some fun with the format, but by the 1990s something had to change as audiences who watched every episode probably got tired of clips. TV was definitely more expensive, if not other issues, and cutting a budget would necessitate a clip show too. To be a fly on the wall... I'm amazed that "The Golden Girls" never did a clip show involving all 4 of their wardrobes, given the sheer amount of costume changes and those costumes were always spectacular...