So we already have an effective way to store heat which can work for decades without servicing and is also cheap to produce (in terms of money and energy consumption).
I actually don't know the answer. I'm just thinking that there must be more to it, if the answer was as simple as "just heat water".
Sure, heat pump hot water tanks are a thing. Air-to-water heat pumps are less efficient than air-to-air as they need to reach higher target temperatures, but it will be more efficient that straight resistive heating by a factor of 2 at low input temperatures, and 3+-ish at high summer temps.
The primary concern would be the quality of the tank’s insulation. I would hope HPHWTs are good on that but if you’re looking into that you probably want to double check the heat loss of the tank.