You are burning fuel, turning a temperature differential into motion, into electricity, transmitting the electricity, then turning it back into a temperature differential.
In the specific application of heating, it makes far more sense to burn the fuel on site, where you are running at far lower temperatures and capable of condensing the exhaust to hit 95% efficiency.
I’ve worked with heat pumps, even built my own custom unit and I know that with the right refrigerants, low temperature distribution and oversized ground loops you can hit as high as a COP of 7. But the average affordable crappy air sourced unit is more like 2-3 and in a Canadian winter will not function at all, falling back on resistive heating at COP 1. And let’s face it, nobody has $20-50k for an amazing oversized ground sourced system and a rework to hydronic floors. They’re buying a reversible mini-split, DIY installing it and being disappointed when their heating bill goes up.
So with a COP of 2 and a power plant efficiency below 50% you are not even back to where you started if you were just burning the fuel in a furnace. And that’s best case, perfect conditions at the plant, no transmission losses, warm day, no Iosses in the heat pump.
It gets worse if your power comes from burning coal like ours does.
I’m just saying there’s no perfect drop-in solution, you can’t just handwave heat pumps in as a magic problem solver. In many cases there are bigger gains to be had from efficient furnaces than a massive electrification program, at least in the short to mid term.