I think appearance on stage depends on how they appear.
How does their appearance compare to their likely appearance in-game? Link in Spirit Tracks is wearing the engineer's outfit instead of the hero's tunic, ergo it doesn't conflict much. (Which is too bad, I had kinda hoped Link would get that outfit as an alt. Tri-Force Heroes also provides some fun alt costume options though, so maybe we'll see one of those...)
The Pokemon on Saffron City are pixelated "retro" looking instead of 3D. If they appeared as playable fighters, they would look very different.
But Pauline in Super Mario Odyssey has an appearance very similar to what you would expect if she were playable. Why would they base her appearance on earlier games where she was far less fleshed out as a character and her design was far less detailed/attractive? Her appearance in the original Donkey Kong was too similar to Peach (blonde, pink dress), so that would be an especially poor basis for her design. While she's not absolutely 100% disconfirmed, she's pretty damn close. And even then, you're not far from arguing that maybe Krystal could be playable or Meta Ridley could be an Echo Fighter. Just because we've never seen an AT or what appeared to be an alt costume and then had that character be playable in the same game doesn't mean it couldn't happen. Sakurai could do it if he wanted. So it's not 100% for those two either. Theoretically.