Similarly, in mild weather, it is more efficient to burn hydrocarbons and turn it into electricity to run a heat pump than use that hydrocarbon for it's heat energy directly.
Pumping heat is more efficient than making it.
Compared to nearly 100% usable energy from normal solar panels.
Furthermore if you have a heatpump you can convert this electric energy into heat energy with a factor of >3 (COP).
I live in Switzerland where these are available. A Cowa 58 [0] costs CHF 4692 [1] and stores up to 13.5kWh. If you're heating the water with a heat pump, that's ~6kWh of electricity, so ~CHF 782/kWh.
I'm in the process of installing a 33kWh battery and the battery + inverter cost CHF 13600 in total for just the hardware, so ~CHF 482/kWh.
If you add solar panels, the inverter does double-duty producing AC from both the battery and the panels. The battery does double-duty producing both hot water and allowing you to use solar energy outside the times when the sun is shining.
That said, having ordered a heat pump recently and being in the process of having solar + batteries installed, the amount of electrical work needed for the solar/battery install is substantially higher than was needed for the heat pump and here, the labour costs quite a lot, pushing the upfront cost difference even higher.
I think that's where these heat storage things fit in: they have a much lower upfront cost. No matter how cheap the battery, for it to be useful in a Swiss residence, it needs to output a substantial amount of 3-phase power (3-phase is standard here, even in most apartments), which means you need to spend a couple thousand Francs on an inverter and electrical work. These heat storage devices are quite cheap and don't even need someone qualified to handle refrigerants, I imagine they could be installed by a normal plumber.
That reduced upfront cost makes them far more accessible than electrical batteries, at least for now.
[0]: https://www.cowa-ts.com/uploads/files/Dokumente/Datenblaette...
Does seem like a lot of added complexity (and likely machinery cost) though.