Need to check my math but a heat pump that can do a COP of at least 2 powered by a 60% efficiency natural gas power plant should be more efficient than a 90% efficient natural gas furnace. That's not even counting a renewable/nuclear mix on the grid or say solar on your house.
Air source heat pumps are technically solar, they take heat from the outside air which was warmed by the sun.
Even better would be geothermal ground source heat pumps but the install costs and complexity are much more.
Electrification has so many advantages since your decoupling and abstracting power source from use, now your car or your house heating is not tied to a specific fuel.
In my area natural gas is 3x cheaper than electricity per kwh, so you might be right that the electric solution you outlined uses less overall energy but the end user will be punished with a higher overall utility bill.
Also, in cold climates where gas heat is typical the overall energy needed to heat the house is very large compared to typical winter electric use, which will likely anger homeowners after heat pump installation.
In my area it's about 2.6x so a heat pump only needs to have a COP of about 2.4 to equal the cost of natural gas per unit of heat delivered when compared to a 90% efficient gas furnace. These modern air source low temp heat pump can maintain a 2.4 COP down to about 17F.
Note my area is pretty warm (FL) so even though I have natural gas to the house for cooking and hot water I do not use for that as my air heat pump works very efficiently in the cool temps here. I have resistive heat as a backup and it never turns on.
Geothermal heat pumps can maintain 3-4 COP year round in any temp then your easily surpassing natural gas even at 3x the cost.
Air source heat pumps are technically solar, they take heat from the outside air which was warmed by the sun.
Even better would be geothermal ground source heat pumps but the install costs and complexity are much more.
Electrification has so many advantages since your decoupling and abstracting power source from use, now your car or your house heating is not tied to a specific fuel.
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