I'd want to see a category for it. Actually did a TotS speedrun today; started timing it after loading in, and ended the time after picking up the Epic Carrot.

I honestly think Fighter's the way to go with a speedrun of TotS, purely because of Lethal Strike's insane reach. Mystic's Blink doesn't go nearly as far (and is just not that great-feeling to use IMO), and any of Bandit's extended dashes cause bonking off the walls, so some jumps that would be hypothetically possible fall a bit short because of that.