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MK does have a Time Trial mode, which is 100% single player. (True it's not really a single player game), I don't know all the modes from ARMS but I believe there is a "single" player Grandprix mode.
However you're 100% wrong about the Single player of Splatoon (2) being an afterthought. It does indeed teach you how to play the game, but it also tells you the story of the game.