Heating with heat pumps is highly efficient and already the cheapest way of heating your home. The grids are ready for it - especially considering the amount of residential solar.
Yes but the major energy consumption of a household is heating than transport than utility.
Using ground heat (deep ones) reduces the electricity need sign.
Also if a heat pumpt creates 3-6 the energy from 1kwh, its even more efficient to burn oil and gas to make energy out of it and remote heat than just burning it locally in your burner.