Here's my restatement of the statistical approach (correct me if I'm wrong):
Instead of proposing some metric for fun that is valid a-priori, we are going to look for the very grounded game-specific correlates of fun and optimize with respect to those. Satisfactorily capturing the entire fuzzy sense of human fun in a finite piece of code is silly, but cataloging the observed feedback for every popular combination of level elements (e.g. "goomba two blocks to the right of a coin block while the player has a fire flower") is both practical and useful for automating level design.
Instead of proposing some metric for fun that is valid a-priori, we are going to look for the very grounded game-specific correlates of fun and optimize with respect to those. Satisfactorily capturing the entire fuzzy sense of human fun in a finite piece of code is silly, but cataloging the observed feedback for every popular combination of level elements (e.g. "goomba two blocks to the right of a coin block while the player has a fire flower") is both practical and useful for automating level design.