Technically it was only a remake in story-only, but regardless I noticed SF is one of the few Nintendo games to have a consistent timeline. (aside from the original SNES game) Regardless, I think they kinda went overboard with the story in most of the later games, (though I still enjoyed them, but the series started feeling like a typical sci-fi series afterwards) after the out of place dinosaur planet story, (I'm aware of the game's orgins as a different Rareware game) the Sci-Fi cliché grimdark Apaaroid story in Assault, (including the killing off of some characters… well sort've, some like Pigma randomly came back) and the schitzophrenic Krystal & shipping space anime drama in Command personally I was glad to go back to a more simple SF64-like story, and bring back the original villain Andross. I don't mind complex stories, as long as they don't distract from the game, and Star Fox is not an RPG, or a movie, and the stories were getting too much at times.
It was nice to get back to basics, with a more simple story, and back to "blowing stuff up," but admittedly, I wouldn't mind going back to the original canon for the next game, or whatever. Also, Miyamoto isn't always against story, as he allows plenty for Zelda, (granted they reboot those games all the time) and Rosalina's backstory in Super Mario Galaxy. Plus some others like Takaya Imamura are just as involved in the making of Star Fox series as Miyamoto is, so I wouldn't just blame him.
As for SF2, when Takaya Imamura was asked if SF2 would be released officially in some form like "Virtual Console," he said no unfortunately. (Not to mention it's difficult to emulate/recreate the Super FX2 Chip digitally on modern consoles apparently. This is why the original SF and other FX & FX2 Chip games aren't on VC.)
To be fair, some of the stuff from the unreleased SF2 was reused in SF64, (all range mode, Star Wolf) Command, (the strategy map, and mini-battles) and Zero. (Transforming vehicles.) So it lives on kinda.
Some also speculate that Bill & Katt were expies of Miyu & Fay. (Though, I wouldn't mind them being canon too. Sega canonized scrapped "Sonic the Fighters" Honey the cat, after all. So Beta characters becoming canon has happened before.)