I'm gazing at my trophy collection and noticed some enemies being trophies but absent in Smash Run, which makes me think: could those enemies have also been considered for the mode? What if they released DLC to include more enemies?
Doing a listing per series, this is what I got:
Super Smash Bros. (SSE): Gamyga, Bytans
Seem to reuse models from Brawl. The trophies are also in the same poses as Brawl, as far as I can remember.
Mario: Piranha Plant, Cheep Cheep, Blooper, Buzzy Beetle, Pokey, Paragoomba, Dry Bones, Thwomp, Boo, Wiggler, King Bob-Omb, King Boo, Ghosts (Luigi's Mansion 2)
Two of those really wouldn't have worked as there's no water and the swimming mechanic is absent in this version as well.
DK: Scurvy Crew, Mugly, Krazy Kalimba
DKCR enemies, pretty much.
Zelda: Like Like, Skulltula
Like Likes were enemies in Melee's Adventure Mode...
Kirby: Bomber, Wheelie, Bugzzy
Bugzzy could be one of those stronger enemies.
Pokémon: Hitmonlee, Porygon-Z, Audino, Sylveon
Those have neither appeared in previous Smash games nor they appear as Poké Balls... Audino could have been interesting if he healed other enemies.
Kid Icarus: Mik, Specknose, Centurions
Those are enemies from since the first game. Centurions appeared late in KIU as enemies as well.
I'm likely looking too deeply at this.
Still, Smash Run finally does something the Smash Bros. series has always poorly done: the enemies cast finally has the crossover feel as the rest of the game. Brawl was especially guilty of this with only having Mario enemies besides original creations.