so my stupid question is, cannot it be used for power? Surely the same system which radiates the heat can be exploited to generate power with something akin to a sterling engine.
Which is fine if you have lots of excess radiator fins. But they almost certainly don't -- shipping up extra radiator fins in order to get power from the excess cooling capacity would be less efficient than just adding solar cells (efficiency of a heat engine maxes out at 1 - (T_cold / T_hot)).