Isn't Intelligent Systems fully owned by Nintendo?
Technically. But they have said in the past that franchises which share ownership (pokemon with TPC and Game Freak, Kirby with HAL Labs, FE with Intelligent Systems etc.) are harder to do licencing deals with because every party has to agree on what to do. Obviously this isn't the case with internal collaborations like Smash, and this hypothetical racer, as these companies and subsidiaries are more likely to trust nintendo proper than some random outside developer.
I can understand the third parties being more difficult to work in though, but not as much as Wade makes it out to be. Capcom and SEGA both have well known policies that all you really have to do is ask the team in charge of the series, and if they're okay with it then the crossover is approved. Namco's policies on this are unknown, but considering it's just Pac-Man in smash so far, and Pac-Man has appeared in the Namco developed Mario Kart Arcade series, I foresee no difficulties. Square is.... Square. And with how they tend to be with approving story elements for crossovers.... I really can't even guess how they'd respond. I doubt anyone has ever even asked to include their characters in a kart racer before. But I tend to believe that they'd be willing due to A) the insane marketing opportunities this game would allow, just like Smash proper, and B) the fact that assets for the required characters already exist thanks to Smash. Microsoft, same thing. The exact details on the specifics of Banjo's appearance are unknown. Including how friendly the companies are with each other and if they'd be willing to work together again. SNK would probably just be happy to be asked, as their popularity has been dwindling and they need the exposure.
At least, that's how I see it.
(jeese, It's like I'm writing an Arlo video)