A modern natural gas power plant has over 60% efficiency of electricity generation. 40% is for rather old ones or those used for peak, not base load. But even t

A modern natural gas power plant has over 60% efficiency of electricity generation. 40% is for rather old ones or those used for peak, not base load. But even those are improving. Moreover, using natural gas at home for heating is not 100% efficient. Some heat is lost with exhaust plus not everything is burned. A good furnace with proper heat exchanger is about 90%, but cheaper ones can be below 80%. So even if your electrical heat pump is just 200% efficient and the electricity comes from a gas power plant, it is already a win compared with a gas furnace at home. Both with electricity and gas there are transmission losses, but they are roughly the same and with electricity we know how to make them smaller long-term.