Electric car chargers are able to vary their current draw to match the homes requirements, there is no technical reason why the same can't be done with electric heating.
Virtually all other methods of heating are preferable.
Not quite, the storage heater is worse, the advantage with the electric boiler is water can store the energy with lower losses too iron laden bricks, so you can heat the water store, and still use it a week latter.
But how much average power is needed to heat a house? In the main the 28 kW gas boiler is installed to work the instant shower, as long as the energy is stored in water, and there would be simply no point in having an electric boiler unless it stores the energy, then a sudden demand due to arriving home for example would be satisfied by the stored energy. So only looking for average power not instant power.
Back early 80's my house had a 4.5 kW gas fire as the only heating, not really good enough, however the problem was time it took to heat house, not keeping house warm, this has been a major problem with the gas boiler, to remove the hysteresis you want to modulate output not switch off/on, so you want the boiler to modulate down to quite a low output, and most will not modulate below 6 kW, so they end up using a mark/space ratio to keep an even heat.
The electric heating also has the problem either on or off rather than modulating although you can have switching between 1, 2 and 3 kW for an electric fire, that seems rare, even when 1 or 2 kW fires are used with thermostatic control, often the user has to select the 1 or 2 kW it is not selected by the thermostat.
We call it a boiler, but of course we don't really boil the water, so in simplest form a cistern with three immersion heaters each set to slightly different temperature can vary between 3, 6, and 9 kW as required, and remove nearly all the hysteresis keeping each room at the temperature selected on the electronic TRV or fan speed if a fan assisted heater is used, and with fan assisted a heat pump can either heat or cool the water store so the same system can both heat the home in winter and cool it in summer.
As to power the Economy 7 traditionally had it's own supply and consumer unit, so there is nothing to stop having a separate supply for the heating.
If solid fuel, gas or oil can be used clearly they are cheaper to run, but the whole idea of the electric boiler being immersion heaters in a tank lends itself to multi fuel. And with solar or wind power the excess can be used for heating, my brother-in-law house would maintain its self at around 14°C using just the excess solar power, the system was designed to heat house rather than export power.
However the installation cost of electric and multi fuel heating systems gets silly, you want the water store above the solid fuel fire so it can thermo syphon, this means reinforced floor to take the weight, and saving energy is all down to control, when the pump runs, etc. It seems the sky is the limit with building management systems, but keeping it simple the circulating pump is powered as if it is the boiler, and the immersion heaters are controlled by the cistern temperature, and TRV heads control each room.
So a house which needs a 28 kW gas boiler with no heat store, will likely only need 9 kW of electric heating because of the heat store. So on return home it can deliver as much as the radiators can dissipate, even with just 40 gallons of water, that is a lot of stored heat, so can deliver 30 kW for an hour, to rewarm house, and 9 kW is enough to maintain the temperature.
The domestic hot water works in reverse to normal, the hot coil has domestic hot water in it heated by the water in the tank, but to heat the domestic hot water fast enough it clearly has to be a very good hot coil, heat exchanger, calorifier which ever name you want to call it by.
The cistern looking at £350 plus and can easy pay £1000, depending on size of house and supply type, may need to double up, so all in all looking at around the £5000 mark to start with and can easy cost 4 times that figure, my brother-in-laws was installed when the house was built, but when he moved and looked at same system in new house, was looking at £50,000 and as he said at 69 it would never pay for its self so he now has no solar panels, and the solid fuel heating is not integrated with the oil and solar heating, the installation costs are just too high.
It can be done, but for most people it is a pipe dream.
