as far as i know, its just another part of the main cooling loop, if it had its own radiator, then it would need its own reservoir and pump for the coolant.
i personally would like to see a true oil cooler where the oil itself is pumped through a radiator in the front of the car, where even the hottest 100*+ air temps would be much cooler than the hot ass coolant running through the motor. but i would immagine that would put a lot more stress on the oil pump, or the thickness due to really cold weather.
now correct me if im wrong, but isnt the trans cooler actually pumping the fluid through a heat exchanger in the front of the car?