I noticed a common theme around here is that the people who diss on Banjo and Kazooie are those who had little to no direct exposure to their games and their influence, so they can't relate to them at all and the significance of their addition flies over their heads. And because we humans are creatures who are afraid of the unknown we require to build a connection over time to get us to care.
As people know already, the crossover appeal of Smash lies in the All-Star cast that makes people want to play as a character they can relate to regardless of moveset or tier placement. And the Smash fanbase is very diverse with people from different age groups. A lot of those people grew up during the SNES and N64 era, and the developer Rareware became a very significant force during that time. As JonTron puts it, they were "the Beatles of the gaming industry"; almost every game they put out was a gem. They rebooted the DK franchise and made the DK Country games, giving that series a very distinct feel from how it was originally envisioned that still influences it to this day. And they also made Banjo-Kazooie which basically took the Mario 64 formula and improved upon it. The character Banjo first debuted in Diddy Kong Racing though as a part of the branching DK franchise and was described as Diddy's friend.
People who harp on the trailer's assets just seem to miss the whole reference. Rareware made the characters K. Rool and Diddy, and they are also responsible for creating Banjo & Kazooie. The DK64 and DK Country were platform games just like Banjo-Kazooie, and BK oftentimes had references to those DK games. They are kind of like sister series. So, in the trailer, DK, K. Rool and Diddy are cheering because they are happy to see them back. Because they are welcoming family back to their original home.
"Random and out-of-place addition" is just a terrible, terrible argument against a newcomer that I thought we outgrew long ago since Snake was added into Brawl. There was a time Banjo & Kazooie were considered 2nd party and became very well associated with Nintendo's colorful cast of mascots, plus people voted for them in polls for a Smash 64 sequel in the japanese website long ago. If that's random and out of place, then you have a completely different understanding of those concepts than I do.
People simply like playing as an icon from a game from their childhoods, so their moveset merely works by just referencing the source material without trying hard to do something to make people say "Woah, I've never seen anyone do something like that before!". Sometimes, simplicity just works.