I'm not sure of to whom you were referring, but I do have an Xbox controller (which my SO uses). It's just imperative IMO in general game design for all menus to use arrow keys, Enter, and Escape, regardless of the actual player controls.
This game could totally use Overcooked's method for two players on keyboard! It uses WASD + Left Control/Shift/Alt, and arrow keys + Right Control/Shift/Alt, along with a couple of other keys.