I want to clarify first that I don't think Sakurai chooses characters based off their home console either, but with Banjo I think it wouldn't have happened if he had originated elsewhere. Its true that Banjo-Kazooie is a great game, and that's why people request him, but if it hadn't been on a nintendo console it would not be nearly as popular among the smash fanbase, which is comprised predominantly of nintendo fans. There are plenty of great, highly praised games out there that don't have characters popular among the smash fanbase. For example, very rarely will you find people asking for Gordon Freeman to be in smash despite Half-Life typically being considered a franchise of exceptional quality. If Half-Life had been a game on the N64, than maybe Gordon Freeman would be highly requested and get a place in smash, since then there would be more crossover between Half-Life fans and Smash fans.
Honestly, I doubt the demand would be any different. Severely amazing games get tons of demand for remakes or the character being used more often. Banjo's legacy as a major character isn't Nintendo-related in itself. It's still the full-out quality of the game. You could've had all the Rareware games(save maybe Killer Instinct at best, and obviously Donkey Kong 64) on the PlayStation at that point and it wouldn't change the quality or enjoyment of the game. The system really had no correlation to his demand.
Master Chief technically has an appearance on Nintendo as a Minecraft skin.
Not even technical. Cameos are official appearances on a system. So yeah, Master Chief has his own Nintendo appearance. It's even called the "Halo Mash-Up Pack", marketing Halo's first official Nintendo appearance.
The debut system has everything to do with Banjo's demand. It's only natural that Nintendo fans would be drawn to characters that were iconic on Nintendo consoles.
It doesn't have as much to do with it as you think it does. Sure, some people only wanted him because of the silly idea that he is magically tied to Nintendo when that stopped being the case a long time ago. But there's a reason why various characters like Crash and Spyro have demand too, and it's not because of some Nintendo appearances, it's because they're gaming icons. Banjo's gaming icon status is pretty much due to major game quality first and foremost. The system would not have changed anything whatsoever. There's a reason the Xbox Banjo game did significantly less well, and it's not the system at all. It's because they didn't make it based upon the regular games by completely redesigned it as basically a spin-off gameplay design. If it was Banjo-Threeie like people have wanted, it would've done way better. There's a reason why Rare Replay has the original 64 titles, due to their high quality, not just cause they were on the 64. If they weren't high quality, it'd be a different story. In fact, if it weren't for the games being high quality, there really would be next to no demand for Banjo. Quality is absolutely the key factor. The Nintendo association was significantly less important and still overall is.
Just saying 'it's an amazing game' is reductive. There's tons of amazing games that have zero Smash demand. Where's the demand for Lara Croft? Or CJ? What about Manny Calavera? Adam Jensen/JC Denton? Gordon Freeman? Pretending that console doesn't play a part in people's wants is very strange.
A lot of those characters have a lot of demand too. Because they're major characters and earned a spot in Smash by being major alone. Actually, every single video game character can easily have a spot in Smash by virtue of being a video game character. Likeliness is a different story. You know many of those have a support thread here for a reason, right? In fact, it's because we decided to not be ridiculous with the rules and allow any Video Game Character to have a support thread because we're already aware that Sakurai doesn't give a rat's ass about a Nintendo connection.
Hell, massive demand for big, successful third party characters seem to end at the N64 era - coincidentally when third party support started to leave Nintendo. When you look at modern third parties, the ones with the most support are Indies, aka the games that do still get released on Nintendo hardware.
This isn't remotely true either. There's tons of demand for characters like 2B, Steve, Master Chief, Kratos, etc. And those are just some examples. The Smash bubble is a terrible example of what's actually going on. The whole logic most care about some Nintendo appearance is actually faulty and is the vocal minority at best. A huge amount of people really really don't care about Nintendo connections these days. What they want is fun playable characters from games they played. Regardless of the system. Again, it's why the support thread rules changed, to reflect the times. Besides that, again, as I've made it clear before, the Nintendo connection is a flawed thing that isn't actually a key factor.