I would however like to see that waste heat being used for something like dishwashers or just being vented out (instead of into the room that might have to be actively cooled).
Water heaters that are also AC units do exist (a heat pump is an ac run backwards)
I could imagine at some point, all our heated and cooled air, water, and ice could be one system.
For fast temperature demands, such as hot water or ice, perhaps reservoirs of chemically stored heat and cold could be built up at useful locations, for very high speed release when needed.
Completely dispense with storing hot or cold air/water, except for fridges. But provide the cool air for them, as a byproduct of being one system, avoiding the local inefficiency of both cooling air in small quantities and generating heat at the same location.
It would make it cheaper to have more fridges and ice makers around a houses, if you just had to plug them into power and an HVAC controlled "inlet/outlet".
Did you know that people do this? The brits love making a cuppa tea. It's free energy and the heat pump in the fridge is already doing the work.
That's an average power consumption of 20W. But electric heaters are say 1200W or 2000W.
Or perhaps you may have missed a nuance in the comments above yours? Nobody is claiming that heat pumps don't work, they certainly require a source of heat to pump though, and the air in a kitchen fridge ain't that.
https://www.homedepot.com/b/Plumbing-Water-Heaters-Tank-Wate...
You could save some power, but not very much.