In buildings with water heating this is already commonly done, accumulating heat in water tanks. Size of water tanks is dimensioned after how much heat you have to store.
Electric heating with water heating is sometimes used in Northern Europe at least, often with a heat pump.
Ultimate would be solar panels on the roof, heat pump to multiply the electricity 3x-5x and water tank storage to last 24 hours.... Never recoup the investment though..
At least in Nordics (I'm from Finland) heat pumps are rapidly replacing other forms of heating. One can get a big enough heat pump for a 200m^2 house (including heating hot water) for around 10-15k, with a few thousand more for installation price.
Adding 10-15kWp of solar panels to the roof is around 6k more. It's definitively a no-brainer as it will recoup the investment in 5-10 years.
Depends on the location, but around here solar for heating is completely useless.
In Germany (which is farther south than the nordics and gets far more sunlight), solar panels are already insufficient for heating half of the year. On a typical single-family home, you will get at most 10kW peak power solar on the roof, which you can reach in the summer months when there are no clouds. In winter, those 10kWp will generate at most 5kWh of energy per day. Which is a factor of 4 to 5 below the 20 to 30kWh per average day for heating (with generous insulation). The farther north you go, the worse this gets. Half of the nordics get essentially no sun at all in winter, and are quite a bit colder than Germany.
So you need something other than the sun to heat your home in winter. A heat pump can double, maybe triple the solar energy you might get on sunny winter days, but that doesn't usually cut it. So you need grid electricity, wood or fossil fuels. And when electricity prices are as low as in the nordics (around or below 20ct/kWh), heat pumps are totally viable.
Adding solar can be sensible for cooling in the summer months, and maybe a bit of hot water, and heating in late spring, early autumn. But for winter? Totally useless.
And while you could do long-term storage, that will cost you several arms and legs, tons of space and a huge maintenance hassle. And if anything should go wrong with your storage, you have no heat all winter and better have an emergency plan...
There's a surprising amount of earth architecture in Germany. The walls are your storage ... not enough to last all winter, and not enough to make your house actually "warm", but enough to provide a baseline that smooths over energy availability issues.
Of course, it works even better with higher levels of insolation, since the exterior surfaces of the walls receive more energy during the day.
tripling the heating/cooling power isn't "needless complexity".
Full solar heating pretty much works if either you have some truly massive roof area or live in place with no winters. Here solar power is at most 1/4 of summer one, at time where you need it most.
Remember, even with free panels, roof space is limited.
I am annoyed how water-water pumps are consistently much more expensive than water-air despise the fact complexity doesn't really change, only the type of heat exchanger (they are just less popular).
Hybrid system where the fluid could be sent to radiator (at night, or in summer when you want to cool) or some solar heat panels on the roof wouldn't be that much expensive, if not for pump costs.
Electric heating with water heating is sometimes used in Northern Europe at least, often with a heat pump.
Ultimate would be solar panels on the roof, heat pump to multiply the electricity 3x-5x and water tank storage to last 24 hours.... Never recoup the investment though..