[eternauta3k]

Waste heat is not free to the degree that you're not cooling your cold side as efficiently. If "sending heat to homes" has the same thermal resistance as "just dissipate it", then sure.

However, I find it elegant that heat is directly used to heat homes, rather than turning it into low-entropy electricity just to turn it to heat again (which is inelegant, even with heat pumps).

[ip26]

Burning natural gas to make electricity to run a heat pump isn’t elegant- but it is more efficient.

We need a heat pump that is heat-powered…

[eternauta3k]

There are old propane refrigerators which do exactly that (heat powered heat pumps).

Have you done the math to check whether it's more efficient?

[ip26]

A natural gas furnace is up to 98% efficient. A natural gas turbine is 40-60% efficient; a modern heat pump can have a COP of 3 or even 4, for 150-200% equivalent efficiency (ballpark).