Also, the running costs of a heat pump are reasonably comparable to gas heating, so you don't even really save money by doing this. (Plus they're more complex and expensive to replace when they break, the installation process is really disruptive and not practical for everyone, etc.) On top of that, a lot of the electricity to run them is going to come from burning gas anyway in most countries. They mostly seem to have caught on in places where gas wasn't plumbed out to so many homes, there are good reserves of dispatchable renewable sources like hydropower, or both.

A combined cycle gas plant has an efficiency of 50-60%, pipe that electricity into a heat pump with a COP of around 3 and you're well ahead of burning the gas directly for heat.

Only if you've fitted each house with a heat pump. Which is expensive.

Even I have trouble motivating the investment in a ground source pump in a really cold climate in Sweden. My regular air-water pump is around £4-7k and has a thermal efficiency (COP) of over 4 (so 1kw electricity is more than 4kw heat) and that’s with no digging or expensive installation.

I get that there is no way Central Europe will switch to ground source, but regular heat pumps should be cheap enough to subsidize.

Heat pump water heating system with simple air outside unit (similar to mini-split A/C), tank, and remote control is about 300k-500k JPY in Japan including construction cost.