ATC operates on my EV just fine, and as far as I can tell the fridge operates when towing too. It must be a car specific thing. Maybe sharing the details of the car may help?
My Toyota PHEV is fully wired for ATC and fridge from the factory. I suspect the issue is no different than for many ICE cars with factory fit tow bars which do not come fully wired?
BusterB
Caravanner