Lot of bad information here...
For starters... No, I’ve replaced my radiator and thermostat, I know how the cooling system works and no, the fact that I’m seeing cooler temperatures is not a sign of a greater problem. My car runs a cool 186-188 during normal operation (thermostat is 82C). It makes perfect sense, you’re just being stubborn.
The fan clutch engagement lessens with increased rpm (more on that to follow) and yes, you will generate more frictional heat at a higher rpm. However, when going downhill in gear, especially a higher gear, your ECU will cut fuel from the injectors if the throttle is not engaged and the rpm is above a certain speed. That’s why it’s more fuel efficient to go downhill in gear than in neutral. In neutral the injectors must continue to burn fuel to keep the engine from stalling. So yes you get more frictional heat but you get less combustion heat. So no, higher rpm does not always mean more heat generated, only more frictional heat. Also, your cooling capacity overall does increase at higher rpm. Ultimately your cooling capacity is what dictates whether or not your car will overheat (talking extremes here). You don’t blow head gaskets because you’re running a car at 2500 rpm lol. The engine is always generating heat, the cooling system is what saves it. Obviously this is the extreme end, but you get the idea. Increasing rpm on the water pump will also help cooling as you’re passing more mass flow through the block and the radiator (even after the thermostat closes there’s slight bypass via jitter valve). Finally, the fan clutch is not an on/off switch. At higher rpms your fan still spins faster, the slip just increases. You seem to imply that above a certain speed my fan will not go any faster. Simply not true.
Anyway, whether or not the engine is getting cooler is a totally moot point, maintaining control of your vehicle and avoiding warping your rotors is the real reason you do it. Going down a grade, especially on a one lane road with a full load or in icy conditions, you absolutely can not ride your brakes. The people on here claiming there’s no reason to do it clearly have not experienced these conditions. If there were no reason to do it or if it were bad for the trans, do you really think the engineers would let me select a lower gear? Don’t you think the FSM would say something about it? C’mon lol. There’s absolutely no harm in downshifting with an automatic, try it sometime.