Wow, this is just handing me a chance to plug on a silver platter
There's actually a lot of highly interesting and unique choices, but here's my top two:
The big one in the Smash fandom is
Golden Sun, whose popularity and reputation as one of the absolute best GBA games is well-known. The game holds up great today and probably doesn't get enough credit for its novel blend of overworld puzzles with classic random-encounter JRPG gameplay. The moveset potential here is massive and well-documented.
I also think
Wave Race could be a very interesting alternate take on the mounted character idea besides the bikers who get more discussion. This had very strong sales for an N64 game, is one of the best-remembered classics on that console just under the top tier of stuff like Mario 64, OoT, and etc., and touts a longterm industry legacy for its revolutionary water physics.
And it has dolphins. This also shares a character pool with
1080 Snowboarding for whatever that's worth.
Among the others worth mentioning (far from an exhaustive list):
Lip from
Panel de Pon could be a puzzle genre rep;
Pilotwings is a commercially successful Miyamoto darling if one could decide on a suitable choice of character and moveset;
Custom Robo actually got some respectable support on the Ballot and sported a fairly long lifespan;
Sin & Punishment and
Eternal Darkness are well-regarded critically, respectively representing arcade-style on-rails shooters and the horror genre;
Starfy and
Chibi-Robo are charming favorites among pockets of Smash fans;
Style Savvy did some pretty significant numbers on the DS and 3DS and represents a unique genre;
Fossil Fighters is honestly a very underrated entry in the monster-collecting genre; even Vince from
Art Academy was recently elevated to AT status and is a representational relic of DSiWare.
Technically these next few are relevant on Switch, but if they got in I'd still see them as strong representatives of that middle period between NES-era and modern Nintendo, with a lot of legacy pull (and anyway I think they're worth a bit more discussion):
The remake didn't move the needle I don't think, and it struggles to make headway in Japan, but
Advance Wars has a lot of critical success under its belt, even if not the best sales. Worth mentioning for its colorful cast of characters, potential soldier-summoning moveset potential, and long history. Also it's a personal favorite.
On pure sales record,
Brain Age and
Big Brain Academy would be squarely in the conversation, it's just a matter of coming up with a viable moveset. Mileage may vary on how people feel about the globular floating mug of Dr. Kawashima or the somewhat amorphous, 2-dimensional Dr. Lobe testing their mettle in Smash, but tackling the edugame genre would make for a unique challenge.
Also feel like mentioning:
Endless Ocean...not sure how you would do a character for this one, unless people were ok with like a straight scuba diver fighter, but a stage with 3D marine animals in the background would be cool. Ashley from
Another Code is a cool representative of the point-and-click genre.
Edit: obviously most of these have little to no chance for a PC (though some I think do have a pretty real chance). I just like talking about them. Though all of them have at least something unique and notable about them you can point to.