^Well, you could argue that TOS helped
invent it, because they did bring back recurring characters like Riley and DeSalle and Martine. And they brought back Harry Mudd, and they tried to bring back Kor in "Day of the Dove" but Colicos was unavailable.
Still, I think the priority behind "Mirror, Mirror" was "dark reflections of the familiar cast" (hence the title), not "alternate reality as opportunity to resurrect dead characters from a year-old episode that most people probably don't remember." After all, at the time, the pilot hadn't been rerun much if at all yet, so audiences hadn't had the chance to get as intrigued by that "alternate crew" and its missed opportunities as we became later on.