This concept was already actively used but mostly abandoned. A friend of mine has a (in Germany) so called "Nachtspeicher Heizung" (lit. translates to night storage heating), the English term is storage heater. https://en.wikipedia.org/wiki/Storage_heater

It is an electric heating system that has high heat capacity stones in it. If you turn it on it will use a fan to output hot air. It was invented to use the overproduction of fossil fuel plants during the night when demand was low. They have a separate meter and cheaper tariffs. With the switch to renewables they could have a second chance.

I believe the main challenge is making then somewhat smart to only store when the energy is cheap, in the past it was a very simple time based system.