No, I'm not arguing that. It the idea of a rad cooler vs a stand alone.
If a rad cooler has a 190 stat in it the engine is going to run at 190.
If I use a stand alone on a cold day I'm not limited by that. Meaning maybe the trans could be cooled to 160, etc,etc. A rad would never allow that.
Except that the engine thermostat controls ONLY the minimum temperature of the coolant in the engine. It has absolutely zero effect on the temperature of the coolant in the radiator. Remember, for the radiator to be doing it's job, the coolant on the cold side of the radiator, where the trans cooler is located, HAS to be cooler than the coolant going into the hot side. If the engine is running at 190, than the coolant on the cold side of the radiator will be running around 180. If the cold side was at that same 190, the vehicle would quickly overheat as the radiator isn't pulling heat out of the coolant.
Contrary to popular belief, there IS a "too cold" point for automatic transmissions. Just like engine oil, the ATF will thicken at colder temps, causing less flow along with shifting and other oddities until it warms up. Anyone old enough to remember driving cars in the 50s and 60s in the colder northern states should be familiar with this - a car that's been sitting in sub freezing temps all night will have a transmission that behaves differently than a warm one. Modern electronic automatics deal with this much more elegantly with variable pressure control solenoids and electronic trans temp sensors.
However, you don't need the ATF to running at 200+ to "burn off moisture". It doesn't need to be boiled out of the fluid, only warmed enough to evaporate the water out. The kicker here is that the cooler temps just means it takes longer. Think of spilling water on hot concrete in the summer - takes only minutes (or seconds if you're in sunny, beautiful Phoenix

) for the water to evaporate off. This will happen fairly quickly even at fluid temps of 120-130.
Getting back to the standalone vs radiator cooler, while in theory the standalone wouldn't be limited to minimum engine temps, it also wouldn't be nearly effective enough to cool that ATF down to 160 unless the trans cooler was the size of the engine radiator as well, due to the difference in efficiency of liquid to liquid coolers vs air to liquid. That's why they are sold as "auxiliary coolers" and not "standalone coolers".