At energy level a heat pump never made sense, it merits are with the fossil fuel transition.
Example, a gas furnace runs at 100% efficiency (103% I believe). Heat pump at 300%. Gas to electricity to home goes at 30%. End to end they both perform at 100%. So on efficiency perspective the gas furnace equals the heat pump - but at a much lower cost.
Retaining the gas network saves us from the massive investments needed in the electricity network.
A gas furnace isn't 100% either (103% is impossible, they lie about what 100% means), and gas to electric can go up to 60%. Heat pumps can also go over 300%, so it's definitely possible for a heat pump to beat a gas furnace.
About the gas furnaces, their efficiency exceeds 100% because of water vapour condensation. It happens both in the furnace and in the plastic exhaust pipe that exchanges heat with the outside air inflow. Gas comes in, liquid goes out and your law of thermodynamics is preserved. AFAIK the majority of housing is using this.
It would surprise me if gas turbines exceed 40% on average, and then the electricity still needs to be distributed. New turbines, probably particularly when using propane could do much better indeed.
My heat pumps all advertise a SCOP of around 5 for heating, and I guess the domestic hot water it would be 2.5 (don't have that, using solar for that myself). And there is a lot the installers can and will screw up, just read some user forums on this. And which consumer actually checks the real COP? So large numbers of heat pumps will perform far from optimal without somebody noticing. The 'screw up surface' of gas furnaces is much smaller. For example, ground heat sources rarely get replenished in summer (not mandatory for residential in my country).
No, your point was on using propane gas to produce electricity for heating. If your consider/complicate the equation with other energy sources (coal, wind, ...) the outcome is more random.
Heat pumps do not make sense unless the energy transition into the equation (wind and solar indeed). But also then, there are major shortcomings with wind/solar currently not yet fixed. For example, my home produces appr. 12 MWh solar energy per year and the heat pumps use a similar amount. Nice balance, but too bad the is a gap of six months between the two.
Example, a gas furnace runs at 100% efficiency (103% I believe). Heat pump at 300%. Gas to electricity to home goes at 30%. End to end they both perform at 100%. So on efficiency perspective the gas furnace equals the heat pump - but at a much lower cost.
Retaining the gas network saves us from the massive investments needed in the electricity network.