Two reasons:
ONE: The skin of the face reacts badly to the varnish of the violin, causing bad irritation of the facial skin in many cases.
Try holding a varnished piece of wood against your face for MANY hours while you are exerting yourself as a string player does when he practices.
TWO: Touching the face directly on the violin affects the resonance of the violin.
I would also think that sweating on the violin over time would damage a valuable instrument.