Wow. The remaining 7,950,999,999 people on this planet now have something to be thankful for, because none of them are as wrong as you.
You clearly did not actually understand what your mechanic told you.
A transmission cooler is exactly what it sounds like. It is built exactly like a radiator and works the same way. It is mounted in front of or next to the radiator for the engine. On a lot of newer cars it is actually part of the main radiator. Transmission fluid flows through it and excess heat is dumped into the air. On many vehicles it's also served by the radiator fan, i.e. for situations where the vehicle is not getting airflow because it's not moving.
The torque converter is part of your automatic transmission literally operates by moving the transmission fluid. There is no separation between the transmission fluid used in the torque converter and the rest of the transmission where the hydraulic valves use it to actuate the clutch bands, etc. to shift gears. The same bath of transmission fluid is circulated through the torque converter, the rest of the transmission, and the transmission cooler.
This is not a truck thing. Even my dinkum Saturn SL I had when I was a teenager that was so pathetic it was literally made of plastic and did not crack 100 horsepower had a transmission cooler -- as designed from the factory. The vast majority of passenger vehicles made in the last half century or more with automatic transmissions have transmission coolers built in. It has nothing to do with towing, either.
Your torque converter absolutely can be locked under acceleration and in fact, nearly all vehicles equipped with a locking torque converter do so as part of their normal shifting pattern when moving up through their gears. This is observable from the driver's seat if you know what's happening. The locking and unlocking of the torque converter feels like an "extra gear" in between the gears. Some Japanese cars from the 80's have a "TC Locked" light on a dash that illuminates when the converter is locked and you can watch this happen in real time. The usual pattern is 1st gear, shift to 2nd gear, lock converter, unlock converter and shift to 3rd, lock converter, unlock converter and shift to 4th, etc. A traditional automatic transmission only has 4 gear ratios, but it will feel like it has seven. Guess why.
Think about it real hard for a minute. A locked torque converter is the same, mechanically, as a fully engaged clutch. If you could not lock the torque converter during acceleration, by the same logic you would not be able to fully release the clutch pedal during acceleration on a manual transmission car, either. It is glaringly obvious that this is not the case.
I am not a "random lemming." I have four decades of actual real world mechanical experience and have disassembled and rebuilt more transmissions, engines, and vehicles in general than you have probably sat in throughout your entire life.