The auxiliary cooler/heat exchanger also serves to warm up the trans on cold starts--important to keep line pressures and such down. Hydraulic fluid does get rather "stiff" in cold temps. .
I really don't see how it can. There is no heat in the coolant rad until the coolant thermostat opens and all that time the trans fluid is shedding its heat into the coolant rad - not drawing heat from it.
There seems to have been a shift away from saddle coolers to heat exchangers (often found at the base of the engine oil filter) that see coolant circulated through them immediately on start-up as in effect, connected to the same circuit as the cabin heaters. That type can warm the trans fluid.
GM didn't go to all the time and cost of developing and installing a heat exchanger in each side of the radiator tank because they thought it was superfluous. Their goal is to keep costs down so they can sell vehicles. As Shurkey has previously explained the heat exchangers use the "reverse flow" concept to heat/cool the oils, and that is the most efficient method to heat or cool a fluid. The coolant flows down in the radiator tanks while the oils flow up through the heat exchangers.
.
OP is concerned with 'high' trans fluid temp of 210F - the same temp as the coolant in my Vortec runs at.
Even the saddle cooler's ability to cool the trans fluid is debatable when its cooling medium (engine coolant) is at a higher temperature than desirable trans fluid temps.