I think the big issue with Star Fox is that is has the Final Fantasy issue.
As a life long fan of both franchises, this is not a fair comparison.
Its easy to point to Final Fantasy and say that it has the "issue" of being radically different each time. This is only superficial, you see. The truth is with Final Fantasy, Square has mastered the art of "the same, but different."
Allow me to explain.
Yes, each Final Fantasy game has its own world, its on mechanics, its own feel. But despite all of that, when you pick up a Final Fantasy game you can expect an RPG. You will always, always, always being fighting monsters to gain XP to level up, exploring dungeons to find secrets, getting new gear and finding new ways to upgrade your party. This is true of every single FF game, from the first one on the NES to the newest one on the PS4. Sure, the exact means of fighting monsters and customizing your characters has evolved over the decades, but despite that you can always count on it building off of the same core no matter what.
Not only that, but the series manages to keep consistent elements throughout its narratives. While yes, Final Fantasy V is cheery and goofy and Final Fantasy XV is dark and somber both games share a few character archetypes, themes, and iconography. And that's part of the core appeal of the franchise. You know that you're probably going to see the same elements you have in previous games, but half the fun is seeing what kind of twist the particular setting of each game puts on it. Sure, some fans have certain styles of Final Fantasy they like more than others, but most life long fans enjoy the series as a whole and not just single entries. This how Final Fantasy has stayed a top-selling franchise world wide for roughly three decades.
Honestly, I could say the same of a vast majority of hugely successful long running franchises. Without writing an entire essay, I completely believe the above holds true for the likes of Mario and Zelda too.
No, Star Fox doesn't have the Final Fantasy issue. It has the Sonic issue.
As you yourself said:
Is it a space drama with animals? Is it an arcade shooter? Is it a Rare adventure game? Strategy hybrid? Is plot important? What kind of tone do we need? How much Arwing should there be? How much on foot should there be? Do we include Krystal or just the 64 cast?
Nobody can agree on the core appeal of Star Fox. It lacks a solid core to work with, you can argue that most of its core comes from SF1 and SF64 but as Nintendo has proven they have no idea how to build off of that core and have very little faith that it can be meaningfully expanded upon or even maintained. For example, thing of how Star Fox as a franchise progressed.
Rail Shooter -> Rail Shooter -> Action/Adventure with beat 'em up elements -> Third Person shooter with rail shoot elements -> Turn based strategy with shoot 'em up elements -> Rail shooter with motion controls
You get the Sonic issue when you start spit-balling. And let me tell you, that list above is some grade-A spit-balling. Nintendo has no idea what the core appeal of Star Fox is, so instead of having a solid core to build off of they've been throwing things to the wall to see what sticks. And so far all its done is divided the fan base over major game play changes that were ultimately spit-balled ideas instead of solid foundations, causing Nintendo to give up and go back to trying to recapture the magic of when the series was most successful.
To sum it up and bring it back to the Final Fantasy comparison: You can point to Final Fantasy VI and say, "This is a RPG about a ragtag group of rebels fighting an evil empire in a steampunk world." And then you can point to Final Fantasy X and say, "This is an RPG about a sports star trapped in a strange world constantly under siege by a whale demon." Despite that, you can also say, "Both games make use of similar character archetypes, themes, tropes and core game play elements to make them into a congruent part of a larger series." With Star Fox you'd be hard pressed to say that.