The end cards are a summation of the MCs impression of his relationship with the 5 main LIs. The fact that he doesn’t include Quinn in this summation suggests he doesn’t consider her one of his main relationships.
From a meta perspective though, end cards are only for us. Why would the MC suddenly take time to think about the 5 LIs at the same time? At the end of chapter 1, he gets tazed. Why at that point would he be thinking about his impressions of them? The only reason it happens then is because the chapter ends which is only a meta thing, to the MC there are no times when he thinks "this seems like a good place to stop and think about these 5 girls I can have a bit of a relationship with, but not the numerous others girls I can also have a bit of a relationship with".
The cards are there as a reminder to the players of the events and interactions with them. He has thoughts throughout the game about all characters, not just the LIs. The end cards are just summaries of them for the player to be reminded of recent events.
If they were an actual thought in MC's head, they wouldn't happen when they do. For example, he for sure would have a summary of thoughts regarding Josy when he leaves for college. At that point in the story he has known her and had a crush on her for all of the time he was working at the store. However since we the players are only like 20 minutes into the game, we don't need a reminder yet.
While I agree that he wouldn't consider Quinn an LI to begin with, he clearly should by now (assuming you pick choices that lead to her). Others would also stop getting them if they were really his thoughts (e.g. Sage shouldn't really have one if you turn her down constantly).
