The factory installed a transmission fluid cooler in the bottom of the radiator, probably because the bean counters told the engineers to do it that way. You don't necessarily have to have a cooler in the bottom of the radiator to operate an automatic transmission. You can mount a dedicated cooler in front of the radiator and run the lines into and out of the cooler.

The nice thing about the cooler in the bottom of the radiator though, is that the transmission fluid is kept at a fairly constant temperature commensurate with the temperature of the radiator cooling water. The advantage there is that the fluid does not get too cool. The fluid has to be up to temp (150-180 degrees F) in order to work correctly and a dedicated cooler in front of the radiator will not have the ability of moderating the fluid temp like a cooling circuit inside the radiator.