Taking the current fad for heat pumps one step further, is there a reason we couldn't have other appliances hooked into circuits of cold/hot/return pipes carrying a refrigerant or coolant throughout the house? For example, your refrigerator or water heater would be just a passive heat exchanger with a thermostat to open and close a valve when necessary.
In the case of a refrigerator, this would mean that in summer, the heat gets pumped to the water heater or directly outdoors, rather than getting pumped into your kitchen by the refrigerator and then pumped outdoors by the A/C. And in winter, the waste heat gets pumped into your HVAC to heat the whole house and not just the kitchen.
In the case of the water heater, this would mean that in summer, you're scavenging heat into your water that would be dumped outdoors by a traditional A/C. In winter, you'd be sucking heat in from the outdoors and from your fridge, and only having to run a heating element to make up the difference when necessary.
Diagrams to illustrate are mine. Yes I know the heat exchangers would be counter-current, but I tried to draw them as simply as possible.
@Clementulus good insight, thanks! To my mind, it's actually *fewer* moving parts to worry about, on account of the fridge not needing a compressor/refrigeration circuit, plus you'd get the benefits of having the heat pump on your water heater without adding another set of moving parts. That cuts most of the complexity out of the fridge, which I'd think would partly offset the costs of installation.
@khird I suppose you are right, assuming you could acquire compatible appliances for a decent price and worked the system into a new building project you would end up saving power at least, and maybe some money too in the end.