In fact, all the four major energy loads in a house - Heating/Cooling, Water heating, EV Charging, House Battery - are extremely flexible.
But we're still lacking good standards for reliable control. Today we do stuff like tell your HVAC to stop via vendor X's cloud API. What happens if your router dies after we send a "stop" command in the middle of the winter?
For many of the minisplits I see control code for, they'd just let the house freeze, waiting forever for another command that'll never arrive.
For critical functions like "keep my water pipes from freezing" / "be able to drive to work in the morning", we need much better standards for reliable control and safe failure modes.