Clip shows were common back then. They started to get scorn since "Shades of Grey" and generally came to be avoided except perhaps for a small flashback here or there. They were purely to save money if a show was overbudget on earlier episodes that season or if they had budget cuts. Think about it- most of the footage was already filmed earlier and it fills a significant chunk of the episode.
Notice DS9, VOY, ENT entirely avoided clip shows. A lot of other shows from the '90s did like X-Files and many syndicated shows. Hercules had 1, EFC had 2 in Season 5, not sure if there might have been 1 earlier, then the Outer Limits had 1 per season (they tried to get creative and weave many of that season's tales together, but most of the time, they fell completely flat), The Legacy had 1 per season and 2 clip shows in its last season! Clip shows seemed more common in cartoons (cartoons seem to like the use of flashbacks more too).
Clip shows tend to always be hated as a concept (though some individual episodes get a mild reception. "Shades of Grey" is presented as a torture session, just Riker and the loathed Dr. Pulaski, basically showing clips from Season 1 to torture Riker. I guess for TOS, a clip show would have been showing episodes like "Spock's Brain", "And the Children Shall Lead" and other bad episodes to viewers). Most get low scores. One of the earliest clip shows, the Leave It to Beaver series finale, seems to be well-regarded. At a time when episodes were aired once and then not seen again til years later, the clip show served to show how much Beaver & Wally grew over the 6 seasons and matured. It was a sentimental look back for viewers.
I always thought they should have gotten creative with clip shows. Show clips from unused footage from episodes, like different angles that were left on the cutting room floor or better yet, whole alternate scenes filmed at the time with all these episodes where the dialogue is changed, the positions of the actors, or even the outcomes, and weave a sort of parallel history kind of clip show. The only show that comes to mind that did something different was Avatar: The Last Airbender, where there was no real clip show, but in 1 episode the group watched a highly embellished stage play chronicling all the events of the series, sort of a spoof of the whole series. That parody served to remind the viewers of all the events while presenting the material in a new way.