I honestly do not think any are likely cuts rn. We really only have one example of a third party actively backing out of Smash which is Konami, and Konami at the beginning of the 2010s to put it elegantly was ****ing imploding. Unless Konami or Square or Sega gets bought out, I doubt we will see any of them disappear again.
It also helps that basically every company in save Terry and Sora (who people here love to forget Sakurai conceded was the most requested character, so I doubt he is as on the chopping block as people think unless for some reason Disney does not play ball, but they did already so...) has another character. IDK how you could be confident that Banjo, one of the biggest fan requests of all time, would be cut when the character that broke Twitter from the biggest video game of all time is from the same franchise as him. Nintendo purists love to imagine a world without Joker, who is from the most critically acclaimed RPG of the past decade. Joker is owned by SEGA, and we have ****ing Sonic and the ballot winner from them too. People bring up how Square is "difficult" because Cloud had only two songs in the base game. Let's ignore how their representation went as DLC and the music can easily be explained due to FF7's byzantine musical licensing. Now that you have one of the biggest gaming franchises of all time in Japan in smash with Dragon Quest, I doubt FF7 is leaving anytime soon.
A lot of the third party cuts talk comes from a place of "purifying" the roster. People want to go back to an era that never existed, where Smash was a game only about "Nintendo All Stars". Even in Melee's development that was not the case: Sonic and Snake, two characters who were in 2001 were very distant from Nintendo were considered. But people are obsessed with "purifying" the roster. Simply put, there is no easy way to predict cuts for third parties because it has only happened once, when a company was imploding. This is the only area that discusses Smash that seems hell bent on cutting third parties. The reasoning for that is obvious: this is one of the last bastions of that outdated mantra of purifying the roster to an era of "Nintendo All Stars". Outside of here, you see people elated about the idea of third parties in Smash. If there is cuts talk, it is much less centered around Third Parties. Even if we do see third parties being cut, we will not be seeing a massive backsliding. If anything, after DLC the next game will probably have even more third parties than Ultimate did.
Unless something drastic happens to any of these companies by the next Smash, do not be surprised if their third party characters show up again.
On the cuts talk, I wish people would realize that fighters are more than just "reps". You can also play as them.
Ice Climber may not be as unique as they once were during Melee but there's still no other character that plays like them. It'd be a shame to remove them just because they're seen nothing but as a "retro quota" fill.
This applies to other characters too, by the way. "Smash fans only buy the game to look at CSS" jokes are a little overdone but it's hard to not make them when so many fans act like movesets are completely irrelevant (or only bring them up to complain about clones).
Smash should provide a wide range of playstyles and treating how characters fight as an afterthought is a bad way to do it.
This. This so much.
People love to float the idea of cutting characters because of some arbitrary rule in their head, even when in Smash history unique characters being cut is the exception non the norm. Snake's compnay was imploding, tech limitations made ICs and PT unviable, and Mewtwo did not make it due to time constraints and Brawl's troubled production. It's clear that Smash cares a lot about preserving all the unique playstyles that are in the game as much as possible. But that's inconvenient for people trying to craft a narrative about cuts.
