I randomly felt like comparing genres to see what's lacking (based solely on their most well known appearances) I will be considering all FE characters under Strategy since I'm unfamiliar with them. Correct me if I'm wrong.
Platformer: Mario, DK, Yoshi, Kirby, Luigi, Peach, Bowser, Ice Climbers, Meta Knight, Pit, Wario, Diddy Kong, Sonic, King DeDeDe, Mega Man, Rosalina, Bowser Jr., K Rool
(Mario x 8)(DK x 3)(Kirby x 3)(Other x 4)
Action-Adventure: Link, Shiek, Zelda, Young Link, Ganondorf, Toon Link, Bayonetta
(Zelda x 6)
MetroidVania: Samus, ZSS, Ridley, Simon
Shooter: Fox, Falco, Wolf, Palutena, Inkling
(Star Fox x 3)(Other x 2)
RPG: Pikachu, Ness, Jigglypuff, Pichu, Mewtwo, Squirtle, Ivysaur, Charizard, Lucas, Lucario, Greninja, Shulk, Cloud
(Pokemon x 9)(Mother x 2)(Other x 2)
Racing: Captain Falcon
Puzzle: Dr. Mario
Strategy: Marth, Roy, Ike, Olimar, Robin, Corrin
(FE x 5)
Arcade: Mr. G&W, Pac-Man, Duck Hunt
Stealth: Snake
Fighting: Little Mac, Ryu
Other: Villager, Wii Fit Trainer, Isabelle
...and then there's ROB and Mii Fighter. I have a big habit of ignoring echoes in these.