I'm seeing a lot of misinformation being spread about the Smash 4 speculation days and that makes me feel old. And because I don't like feeling old, I'll try to clear things up since I was very much here at the time.
The first thing to keep in mind is that the Smash 4 speculation era was broken up into distinct segments. The first segment was 2008-2011. This was the post-Brawl era where we had no idea what would come next. Next was the post-announcement era of 2011-2013, going from after the games were announced at E3 2011 to when they were first shown at E3 2013. Following that was the main period of 2013-2014, which was obviously post-reveal pre-release. Then there was the Ballot era, 2015-early 2016 with the release of Corrin and Bayonetta.
The post-Brawl era was a veritable wild west because nobody knew anything. As such, a lot of the characters brought up were Brawl era characters that didn't get in. Ray, Isaac, Starfy, Saki, Little Mac, Ridley, K. Rool, Micaiah, Geno, and Mega Man were all pretty popular. Even Louie and Jill from Drill Dozer had some support. Geno and Mega Man were pretty much the only super popular third parties at the time since most of the focus was still purely on Nintendo characters. There was some support for Bomberman and Simon, but mostly from people who opted to cut Snake since, at the time, people didn't think more than one character per third party company would happen.
Then came the post-announcement era. This was when I joined Smashboards. Prior to this point I'd been mostly lurking Gamefaqs and YouTube. Now that people knew not one, but two games were in development, we had a little more to go off of. The passage of time killed off some of the previous fanbases pretty hard. The big ones that remained were Ridley, K. Rool, Mega Man, Little Mac, Isaac, and Geno, with those other ones beginning to wane. We also started seeing support for Ghirahim, more support for Mewtwo's return (prior to this, there was a much stronger mentality of "once it's cut it's gone for good), very strong support for Palutena, and some stronger Mario character support (though there was still hesitance from many due to Mario's core four being "all it needed," Bowser Jr. and Toad had quite a bit of support...Rosalina and Waluigi had very minor support due to being seen as "unimportant"). Chrom, Takamaru, Zoroark, and Shulk also started seeing support. Pac-Man became a hesitant what-if when it was announced Bandai-Namco would be helping to make the game. Lots of fear for GA Pac-Man. Smashboards had its "Elite Four" at the time, which was Ridley, K. Rool, Mega Man, and Palutena, with Mewtwo as the Champion. Those who didn't count Mewtwo due to being a veteran moved either Ridley or Mega Man to the Champion spot and added Little Mac to fill the blank. Those six were EASILY the characters with the most sizeable support on this site. Geno was waning.
Next was the main era between the first trailer and release. Villager blindsided people because while people before now very much agreed that Animal Crossing should get a character, Sakurai's dismissal of them in Brawl was thought to be a death sentence. Mega Man got announced and people were very hyped considering his standing in the community. Wii Fit Trainer caused a lot of "wtf" reactions and people assumed she'd be our wacky Game and Watch/R.O.B. character. Rosalina upended Mario speculation. Little Mac got in and people were hyped, another big request like Mega Man. Then came the April Direct and alongside adding Greninja and basically cementing Gematsu, it also killed Ridley. Some still clung to hope. E3 confirmed Palutena, another big want, Pac-Man was hypeworthy due to explicitly NOT using the Ghostly Adventures design, and the Miis certainly existed. Robin and Lucina got in and Chrom died, leaving me very, very sad, but also it was another big name dead. Then Shulk got in and since he was pretty requested people were pleased, despite the odd-in-retrospect rivalry Shulk and Isaac fans had. Before that, though, the ESRB leak confirmed the rest of the roster. No Mewtwo. No Ridley. No K. Rool. Several popular veterans cut only for Dr. Mario to return. Only half of the really big six, and arguably the three BIGGEST of those six were missing. Geno's absence shocked precisely nobody because his support was almost dead at this point.
Whoever says K. Rool only started getting big in 2014-2015 either wasn't there or is misremembering. K. Rool was highly requested since right after Brawl released, if not immediately after Diddy got in. Yeah, Ridley was louder...but that was because Ridley actually had detractors. So shouting matches happened often. K. Rool didn't have that because K. Rool support was practically universal . Most people just accepted that he was in, so it blindsided so many people when he wasn't, especially after the Kremlings in Smash Run reassured those who were worried about Gematsu not mentioning him.
Then came the ballot era, after Mewtwo struck back and Lucas was announced. Lots of third party support threads went up, especially after the Roy and Ryu datamine. This included Banjo-Kazooie, who became fervently requested for the first time after Phil Spencer gave his blessing. On the first party front, Inkling had a very strong showing of support. Other than that and some smaller showings by Elma and Waddle Dee, most first party non-veteran support on this site was the usual suspects: Ridley and K. Rool. The two big (hah) omissions.
And after that, Ridley support grew VERY quiet, having been demoralized after Smash 4 and Sakurai's statements.
The claim that Banjo, K. Rool, and Ridley were EVER the "Big Three" is a total fabrication. The three never had a moment where all three were simultaneously the most supported characters, with Banjo's support starting especially late in the game, after Ridley's plummeted.
Ridley and K. Rool became as big as they were due to years, over a decade, of organic support from the community that exponentially grew. They started big AND ended big. They became popular before there was a "Big Three" or four or five or what have you.
And frankly, there will likely NEVER be another "Big Three." There doesn't even have to be. The fact is that now that the floodgates are open and so many long-standing requests are in, people's tastes are too diverse to collectively come up with a distinct group of big characters. Probably the character with the biggest clout right now is Waluigi, being loved by casual fans and hardcore speculators alike, but even then he doesn't match the heights of Ridley and K. Rool (I'd say he's closer to Smash 4 Little Mac and Palutena: pretty much the next level after, but not Ridley and K. Rool level).
So no. There is no Big Three. Anyone that would've been part of it is already in, and they're not gonna fill those vacant positions.