Heat pumps have greater than 100 percent efficiency when compared to a regular resistive electric heater (which is already 100 percent efficient, when measured as heat out / energy in).
Everyone always forgets about the part where you're cooling down the outside...
Yes. Heat-pumps will make up for some losses from all other steps but I highly doubt it all togrther will reach efficiency of purely thermal system. Heat pumps also rely on access to medium that they cool down to get the additional heat and are at least as complex as a fridge or air conditioner.
It might be that one or the other is better "in general", but I can see that this technology could have benefits in certain scenarios, maybe long term storage in remote, cold climates.
No current electric battery technology has the energy density to heat a house all winter economically. You'd need a volume of batteries similar to the volume of your house.
