[sokoloff]

American style options are inherently more valuable. Imagine you had options on a stock that experienced a sharp but possibly temporary move. As a holder of an American style option, you could benefit from that temporary move, making it more valuable.

[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).

[im3w1l]

The way the market is typically modeled, temporary moves are not a thing.

[sokoloff]

The way the market actually exists, temporary moves are definitely a thing.