As Gary Hearl points out, ATF is designed specifically for automatic transmissions; the oil has properties to cope with the application.
You might find this point interesting
One of those properties is to absorb (entrain) air bubbles. This leads to sponginess (compressibility) in the oil.
I have worked in the fluid power (hydraulics) industry all my life (and still at it). Occasionally we will receive a high pressure (10,000 psi) hand pump & ram assembly (with ATF in the pump reservoir) in for repair because it won't reach full pressure (will only get to 7,000 psi), and / or won't hold under load (it sags down).
The solution is to replace the ATF with mineral oil (10 - 32 cSt); the pump will then reach 10,000 psi, and the ram will not creep down. this takes all of 5 minutes.
The reason is the presence of air bubbles in the ATF, which is doing what it is designed to (capture the air).
As far as using ATF in primary drive cases, i don't. the recommended mineral oil does the job best. It is a higher viscosity (thicker).
Richard