It's not even correct. It's much more efficient to use a heat pump.

Heat pumps may be more efficient, but they can't be employed everywhere an electric resistance is used. To be fair, miners can't either, but are much easier to deploy.

We don't need to think solely of miners - crypto-mining is just one form of monetizing computing. If we could have something like a reverse Amazon Mechanical Turk, we could put computing resources available to receive and process packaged workloads cheaper than, say, an EC2 Spot Instance could, provided the client can cope with the added latency. As for incorrect answers, it could use some consensus where you send the payload to two independent parties and, if they don't match, you send it to additional parties until your consensus is ready.

There are no applications I can think of where crypto-heating works, but a heat pump doesn't. Miners are a lot more difficult to deploy than a heat pump - they need an internet connection, they can break down, they will eventually need to be upgraded, etc..., whereas a heat pump is pretty much once-and-done, and you'll maintain it once every few years.

As for your second paragraph, will it ever be cheaper to do a computation twice independently than once in a trusted party? I'm sure there are a few situations where that's the case, but I struggle to think of them.

Here are two scenarios when a heat pump is harder to deploy: 1) Heat pumps need access to the outside cold reservoir, for example they don't work entirely inside a closed room, where an space electric heater would be fine. 2) If the temperature gradient is too large, heat pumps are less efficient than a regular heater. So many heat pumps fall back to a regular heater when the outside gets too cold. If it is very cold all the time, a heat pump would not make any sense at all. This is why they are deployed mostly in places with mild winters.

This is flat out wrong. Heat pumps are only practically efficient within a range of temperature differentials.

You already need the heat, might as well help launder some money ;-)

More or less. I guess there’s incentive issues too. Maybe now people keep their houses unnecessarily warm to mine more —- but again, this is the closest thing to any kind of justification I’ve ever heard.

Now all we need is a way to make that boiler lined up with top-process silicon costing thousands of dollars per square inch cheaper than the one that uses an electric resistance.

And do that for the environment!