I’m not quite sure we even have the know-how these days for fully analog control systems.

My dumb refrigerator has a circuit board controlling the compressor based on temperature sensors.

My dumb gas water heater has a digital control unit even though it doesn’t use AC or battery power.

Same thing for gas furnace - control board running fan and gas igniter+valves. This isn’t just relays…

It’d be a substantial effort to design analog drop-in replacement parts - if even possible. Installation probably wouldn’t be pretty.

At least I think my toaster and rice cooker are fully analog.