Scotty's grief over Ensign Prestion makes more sense when you know it's his nephew. Saavik's emotional side makes more sense when you know she's half Romulan.
I'm not saying a movie is better for being longer. There are plenty of films with ridiculous amounts of padding. (TWOK might have only been a few minutes longer with those character bits intact.) There are plenty of films that have arguably been ruined, because the only mandate was one from the suits in the front office to make it shorter, not trim the fat.