LookingUp: Can't understand why all appliances don't come with an Ethernet port for remote control - I'd certainly pay a little more for a remote controllable option!
Immediate thoughts include heat pump, oven, electric blankets, and I'm sure there are 101 other great ideas.
It really comes down to cost, both product cost and support costs. It would be fair to say that refrigeration engineers and electricians mostly don't understand automation and supporting products like this would be problematic.
I work in commercial building automation and the level of understanding there is low let alone one man bands hanging heat pumps. For them 5% of customers (at most) are interested in this type of solution so why would they bother? There is no margin in heat pumps and is a volume based business. If they have to provide lots of support then that cuts their margin further.