They also have mouth, ears and hairs...
Why do only knights have eyes and nose on the board?

Tradition. When Nathaniel Cook designed the original "Staunton" set in 1849 this is how the pieces looked, and it has become the tournament standard. I've got sets with very elaborate knights, and sets with very abstract knights without eyes or nostrils. All of them pass for tournament play today.
For me the knight is the piece that makes or breaks a set. I've found excellent sets I couldn't buy because the knight was too hideous. Usually it's the wooden sets with poor quality knights but many of the "traditional" tournament sets are bad as well.
Why do only knights have eyes and nose on the board?