[FabHK]

By put-call parity, C - P = S - df K, thus C = S - df K + P > S - K.

This is contingent only on the discount factor df being <= 1, and P >= 0, which is basically always the case. Thus, the value of the call exceeds the exercise value, making exercise never optimal.

Exercise for the reader: Understand why the same argument doesn't work for puts (or calls on dividend paying stocks).