>> more efficient to just burn the fossil fuels on site.
You forget exactly how efficient a coal-fired powerplant actually is. Love or hate them, they have 100+ years of technological innovation to squeeze every watt out of coal. Your fireplace at home is not nearly as efficient. So an electric heater powered by the grid is almost certainly more efficient than burning your own coal at home in an inefficient stove.
A good oil-burning heater has over 90% efficiency. Even no so good and cheap one can get over 70%. The best industrial electricity-generating plants that runs on oil has efficiency bellow 60%.
Does that oil-burning heater need oxygen? If it does then it needs ventilation, air movement in/out of the house, pushing that 90% efficiency number way down.
Efficiency wise, the comparison between a heat pump and a furnace depends on the outside temperature. Heat pumps lose their efficiency for high ∆T, so for winter in a Russia, a furnace is likely the better option
90% is overtall efficiency including losses due to ventilation. Such system with its heat exchangers is not cheap, but long term it pays off compared with less advanced heater.
You forget exactly how efficient a coal-fired powerplant actually is. Love or hate them, they have 100+ years of technological innovation to squeeze every watt out of coal. Your fireplace at home is not nearly as efficient. So an electric heater powered by the grid is almost certainly more efficient than burning your own coal at home in an inefficient stove.