That's not true. Heat pumps are cheaper to run than gas heating, I removed my old single room gas heater for a ducted split system total cost reduction was 30% even before Russian invasion caused gas prices to spike. And house is much warmer.

Gas boilers generally produce much hotter water, so the radiators they use tend to be small.

Heat pumps gain more efficiency if you can reduce the output temperature. So running a heat pump at max efficiency through radiators designed for a gas system, won't put out as much heat into the room.

So you have two options, increase the size of the radiators or increase the insulation. It's better to increase the insulation as you gain the benefit of both warmer room and less energy required to heat a room.

I think that depends a lot on location dependend prices. I am in denmark and my ehat pump is significantly cheaper to run than the gas boiler that it replaced, even if you compare it with pre ukraine/pre covid gas prices.

which begs the question - why would anyone switch from a gas boiler to heat pump then, if they only consider economic utility, and none of the externalities?