It's a very old idea which is in use in many places [1] -- and not just for nuclear plants. Main constraint is that you really can't transport the waste heat very far.

[1] https://en.wikipedia.org/wiki/Cogeneration

Although an advantage of these smaller plants is that they can be located closer to where the heat is needed.

Yes, ideally all the energy released by the reactor would go into the turbine. But no engine is 100% efficient, and waste heat is inevitable. Waste heat is "free" energy in the sense that it would have otherwise not been harnessed for something useful.

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).

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…

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?

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).

How does this work with solar panels and wind turbines?

I know that fossil fuel plants have a lot of waste heat that enables cogeneration, but I've never heard of that with solar or wind.

A fossil fuel plant will burn fuel to produce heat. Some of this heat will be used for generation, and the remainder is waste heat. A solar panel or wind turbine, on the other hand, does not produce significant amounts of heat in operation - a PV solar panel would only get somewhat warm, a wind turbine would only achieve some friction heating - to where it is not economical to harness this relatively small amount of energy (compared to waste heat from an exothermic generation process, like nuclear fission or hydrocarbon combustion)

Solar panels are super thermally inefficient generally speaking, collecting about 20% of the energy that hits the panel. They are dark, and this leaves a lot of heat available for the gathering. You can get solar systems that heat water as well, especially in rooftop solar. This also cools the panels down and makes them more efficient. Not much, but measurably. Something like this. [1]

Of course, in the winter in Canada, you have to bleed the system otherwise the water will freeze in the tubes and they'll burst.

There's no free heat from a wind turbine.

[1] https://dualsun.com/en/product/hybrid-panel-spring/

Actually, wind turbines do produce heat but we generally let it dissipate. It may be that it is not really usable, but wind turbines that only produce heat are a thing historically:

https://www.lowtechmagazine.com/2019/02/heat-your-house-with...

I think the issue is you can’t really move heat too far physically, and turbines are located usually pretty far from houses themselves. Certainly relative to rooftop solar.

No argument here, I was just being a pedant really

I appreciated your comment because I hadn’t actually thought about that before!

My memory from the old Swedish nuclear debates is that the generated waste heat is about as much energy as the generated electricity.

There was talk of heating cities with the waste water, but "nucleophobia" killed that idea, as usual.