New ask Hacker News story: Ask HN: Why not natural gas powered heat pumps?

Ask HN: Why not natural gas powered heat pumps?
5 by derekp7 | 0 comments on Hacker News.
It has been said on here previously that it is more efficient to have a gas powered generator that sends electricity to a house, to run a heat pump, then it is to heat the house directly by burning natural gas. My question is why not both? Use natural gas to the house to run a combustion engine, that in turn runs the compressor on the heat pump. And use the waste heat off the engine to also add to the home eating. Wouldn't that be effectively a very efficient way to heat a home (compared to direct natural gas, or electric heat pumps that run from non-renewable electric source)?