All the post-TOS shows expanded and deepened main cast, leading to episodes being able to be centered on various characters. TOS had a smaller and more focused cast. It was a rarity to even have a Spock or McCoy centered episode, and I can’t think of an episode where at least one of the main trio wasn’t the most prominent character.
I think it’s just a difference in writing styles of the different times between the 1960s and the 1980s. Even look at something like STIV: The Voyage Home. Same characters as TOS, but written in the 1980s and a lot more comfortable giving various non-trio characters their own individual adventures.