I decided to make a very not well researched analysis determining the biggest character omissions in the general audience's view. Here are the biggest omissions by series/category from what I've seen (with some dumb side commentary):
Mario/Yoshi/Wario: Geno, Toad, and Waluigi
These three have always had support from Brawl and onwards.
Donkey Kong: Dixie Kong
She's seen as the last missing Nintendo all-star by many, not that I agree but whatever.
Zelda: Literally anyone
There's not really a consensus as to who should be added, but Zelda has a varied cast much like Mario, Pokemon, and Fire Emblem, so it should not be a problem at all. "But the cast isn't consistent, and somehow Pokemon and Fire Emblem's apparent reason for getting so many characters doesn't apply to Zelda for some contradictory reason," OK, strawman.
Pokemon: A fully-evolved grass starter
The fanbase will advocate for every grass starter until one is finally added. Expect Torterra support threads when Diamond and Pearl are remade.
Kirby: Bandana Waddle Dee
I'm pretty sure Bandana Dee was viewed in the same camp as Inkling and Ridley as an inevitable first party character before Ultimate.
Star Fox: Krystal
She peaked in Brawl, demand for her in 4 died out. I guess it was a big enough peak to get her added in Ultimate as an assist trophy.
Fire Emblem: Lyn
Claiming that anyone else is the big Fire Emblem omission would just be wrong.
Animal Crossing: Tom Nook
I genuinely thought he was getting added as an echo after Isabelle's trailer.
Xenoblade: Rex and/or Pyra
In (hopefully) a few months it might be harder to tell, but at the moment Rex and/or Pyra are still the most wanted Xenoblade characters.
Contemporary (at the time) First Party Character (Metroid, Pikmin, Wii Fit, Splatoon, F-Zero, Mother, Punch Out?): Spring Man
He's kind of dead in the water now but by the next game he's going to get traction back as the contemporary pick.
Retro Character (G&W, ROB, Ice Climbers, Duck Hunt, Kid Icarus, Punch Out?): Takamaru
He's kind of dead in the water now but by the next game he's going to get traction back as the retro pick.
Sega: A Sonic character
I don't think the general fanbase really gives a **** about any other Sega series. Puyo Puyo and Yakuza are somewhat wanted while "give us more Sonic" is a common sentiment.
Konami: Bomberman
Many tears were shed when his assist trophy was unveiled.
Street Fighter: Chun Li
She's the type of character I think many view as a necessity at this point.
Capcom: Phoenix Wright
This one was the hardest I was able to pinpoint. Phoenix was a popular pick before Ultimate opened the doors to other Capcom series like Devil May Cry, and even then he's maintained support and I believe is more demanded than Amaterasu and Dante.
Namco: A Namco character
I'm surprised KOS-MOS gained as much traction as she did before FP5.
Random Third Party Character: Crash Bandicoot
Crash is a very common pick in prediction lists and that's been the case since Smash 4 DLC speculation.
Other absent characters that don't really fit with any of the above: An indie, dead Nintendo series characters, Sora
An indie rep has been demanded since 4. Golden Sun, Advance Wars, and Rhythm Heaven aren't active enough to be contemporary but aren't old enough to be retro either so I'll just stick them here. I don't know what's the deal with Sora.
I couldn't decide on a character for Square Enix, Microsoft, and SNK. Considering that a lot of these characters are already in the game in some form, it's no wonder third party demands are the craziest they've ever been.