[pedrocr]

Amazingly a modern heat pump running on electricity generated by 100% gas is more efficient at heating than burning the gas for heat directly. Modern heat pumps are 5x efficient so you break even at even just 20% thermal efficiency of the power plant and gas plants are much more efficient than that. If you use the waste heat of the power plant for something else useful it's even better. Switching everyone to heat pumps would help even if 100% of your grid electricity was obtained by burning gas and obviously pretty much everywhere does much better than that.