I'm not sure how much that applies to Star Fox. I don't think most players would be more attached to levels like Titania or Bolse than levels like Macbeth or Area 6, the harder levels are seen as more continuations of the main story.
If you want Star Fox to be closer to what others have called "furry Mass Effect" and be one 40-hour story, then asking people to replay it doesn't work as well, though at that point you're asking for a AAA game that's going to need much better sales than contemporary Star Fox has gotten to make back its budget.
I don't think asking people to replay the game inherently prevents the team from doing more with the storyline, progression, or content, though. Nier: Automata is an example of a game that manages to deliver on these aspects across multiple playthroughs, and while Star Fox would have to do so differently, it's not an impossible task to structure the game to accomodate that. They could do multiple scenarios where you play as different characters that reveal different aspects of the story, or structure it as Star Fox team being assigned to different campaigns of the Lylat Wars, or they could hire Kotaro Uchikoshi and let him come up with something wacky. There's plenty of directions for Nintendo to take Star Fox in, and I believe there's room for them to keep the idea of multiple runs if they want.
I think it applies to Star Fox in that it's less being attached to certain levels, but being attached to your first 'whole' playthrough of a story. It's why, in story-based games with 'good' and 'bad' endings, getting the bad ending your first time around often feels worse than if you go out of your way to get it in another playthrough. Because it's not "your first playthrough."
As for the rest, I agree. However, the concept being discussed here is branching paths, not simply replaying the game. NieR: Automata is essentially just 3 linear (with side stuff) campaigns and an epilogue with a bunch of content being shared and added on with every different campaign. You're replaying a fair amount of content, but it's all linear and there's no branching paths throughout.
Personally, and hear me out here lol, I think a game to look at to solve this issue would be Resident Evil 2 (Remake or OG). The game has essentially 4 different 'routes' to go through. LeonA -> ClaireB and Claire A -> Leon B. Choosing to play Leon's campaign first drastically changes the Claire campaign you do afterwards, and vice-versa. In the original, certain things you did in your chosen A route even had an affect in that B route. So, if you opted to sacrifice some ammo in the A route, it would be there to make the B route easier. This could be the equivalent to Star Fox's "Mission Completed vs. Accomplished" thing, with your actions and choices in a level during your A campaign making certain things in the B campaign harder or easier.
In all cases, the first 2 routes you do present a complete and satisfying storyline, running at around 12-14 hours. You're heavily incentivised to do so because, if you don't, you can't even beat the final boss and see the actual ending. However, if you want more, you can choose to pick the character you played second, first, and experience two more similar yet still fairly different campaigns. I think Star Fox could do something really similar and succeed at it if done right.
Sorry for the long post lol