For swimming pools, which are admittedly a special case, heat pumps are already cheaper to operate than gas heaters in most of the country.

(They’re special for several reasons. A big one is that they have huge thermal mass, so your heat pump can operate at whatever time of day you want. This means you can optimize for electric rates vs outdoor temperature. Heat pumps, unlike gas boilers, are considerably more efficient when it’s warm out.)

I heard that a long time ago and thinking back on it, I think it was due to the fact that most electricity comes from burning other stuff so the overall efficiency of burning something to make electricity (definitely not 100%), then transporting over lines to your house, then converting that into heat to warm your home is less efficient than just burning it at your house and using the heat directly.