I figured this would be an interesting topic. As for my ideas:
Routes
• Daisy: In Search of a Super Star (fights every Mario character, ending with Bowser/Giga Bowser)
• Falco: Personally, I prefer the air! (fights characters who have more than two jumps, ending with Rathalos)
• Mr. Game & Watch: A Long Legacy (fights characters in reverse chronological order from the Switch era to the NES era, ending with Dracula)
• Pokémon Trainer: When Eyes Meet (fights characters who join the player after starting as an enemy)
• Sonic: Just a Bit Too Slow (fights characters who played a role in the Subspace Emissary, with a fight against Galleom midway)
• Olimar: Size Matters (fights big characters, ending with Bowser/Giga Bowser)
• Robin: Master of My Element (fights characters associated with Robin's tomes)
• Cloud: In It for the Money (fights characters who were DLC in Smash 4, fighting Master Hand and Crazy Hand midway through)
• Hero: A History of Heroism (fights characters from JRPG's in general)
• Banjo-Kazooie: Class of '64 (fights characters from N64 games, ending with Ganon)
• Byleth: Let the Lesson Begin! (fights characters mirroring FE gameplay mechanics)
• Min Min: At ARMS' Length (fights characters with slowly increasing range, ending with Master Hand)
• Steve: An Unlikely Icon (fights characters from Nintendo and other 3rd party companies)
• Sephiroth: Fatal Fantasy (fights characters referencing the first 7 Final Fantasy games, fighting Marx in Round 6)
Bosses
• Samus: Fights Rathalos in the Final Round
• Fox: Fights Marx in the Final Round
• Jigglypuff: Fights Master Hand after sorting out Giant Donkey Kong in the Final Round
• Peach: Fights Giga Bowser in the Final Round
• Sheik: Fights Galleom in the Final Round
• Dr. Mario: Fights Marx in the Final Round
• Roy: Fights Ganon in the Final Round
• Meta Knight: Fights Marx in the Final Round
• Pit: Fights Dracula in the Final Round
• Wario: Fights Dracula in the Final Round
• Ike: Fights Dracula in the Final Round
• Lucas: Fights Dracula in the Final Round
• King Dedede: Fights Ganon in the Final Round
• Wii Fit Trainer: Fights Bowser/Giga Bowser in the Final Round
• Little Mac: Fights Bowser/Giga Bowser in the Final Round
• Palutena: Fights Ganon in the Final Round
• Shulk: Fights Galleom in Round 6, moving Mega Man to the Final Round
• Bayonetta: Fights Rathalos in Round 6, moving the Pits to Round 1
• Ridley: Fights Marx in the Final Round
• Simon: Fights Dracula in a Team Battle with Richter in the Final Round
• Richter: Fights Crazy Hand in the Final Round
• Incineroar: Fights Giga Bowser in the Final Round with the help of Greninja