Here are my thoughts.
The routes in a game do not need to contribute to a “main story” in order to be good, I think. All of the routes usually share some theme.
Kanon: The central theme is miracles, promises, and wishes as power
AIR: All of the routes have to do with motherly love in different forms. Kano’s older sister acts as her mother, Minagi’s arc centers around her mother, Yukito is sent on a quest because of his mother, Kanna’s arc is about her meeting her mother, and the AIR route is about Misuzu and her aunt Haruko. They don’t form one narrative, but they are a collection of stories that explores a certain theme.
CLANNAD: This is sort of the same way. All of the arcs either focus on family, or community as family. Those are the central themes of the VN. The light orbs unify them in canon.
The anime sort of leaves out the parts about “community” but it’s there in the VN: how Nagisa’s health is tied to Akio’s special place, how the wishes of the town contribute to the light orbs for Tomoya, and special side arcs like Koumura’s IIRC.
Little Busters!: The arcs don’t have a central theme besides maybe friendship? But they are tied together by Refrain.
Rewrite I think is the weakest in this regard since there’s no real connection besides "lol Kagari needed to see the routes happen to make Terra route happen, no central themes, and the tone is all over the place
TL;DR: I don’t think the unity of canon of the story is quite as important as the exploration of the themes in the work as a whole
