The issues are more long term than short, it's kind of like running veg oil / waste oil in a diesel. Sure it will work but for how long and what overall cost?

Flat towing speed with a automatic is limited due to lack of oiling and planetary speed.

With the engine running you will still have oiling but won't be able to overcome planetary speed.

In a automatic trans, planetaries are locked and not spinning in top ( 1 to 1 ) gear relative to the sun and ring gear. Unlock everything and spin the drive shaft and they will now be spinning relative to the sun and ring gear.

What spins / how fast varies on the transmissions make up. The next time someone is rebuilding a trans, turn the output shaft and look at the gear train

Now, before someone says that Saturn cars are commonly towed behind a motor home, be aware that these transmissions are not of planetary design, they look more like a manual trans with clutch packs rather than sliders / syncros.

Other makes are towed, but they typically have a disconnect axle / drive shaft mod.