Heat pumps require a significant capital investment which would have to be recovered on only their efficiency improvement, since they don't otherwise generate revenue.

The math is different for new construction. There heat pumps make a lot more sense because the capital cost is relative to some other heating system you don't already have. Then the higher efficiency will generally cover the relative capital cost even if it wouldn't cover the total capital cost. This might still be less profitable than mining cryptocurrency (depending on a variety of factors) but better than any other traditional heating system.

No it isn't. I know because I looked into it.

Assuming the price of bitcoin doesn't rise or fall, a cutting edge bit of dedicated bitcoin mining hardware will pay for itself in 3 years if operated continuously on free electricity, and will be effectively obsolete in 5 years, as difficulty increases and rewards drop.

So if you only operate the hardware 50% of the time it'll be obsolete before it's paid for itself.

What you want is a cryptocurrency that ASICs are no better at than CPUs or GPUs, so can use an ordinary CPU or GPU that will pay for itself more quickly because most of the mining cost is electricity instead of hardware. (Hint: the hardware you want in this case has the best performance/$, not necessarily the best performance/watt.)

Tom's Hardware did a list for GPUs:

https://www.tomshardware.com/best-picks/best-mining-gpus-ben...

"Which cryptocurrency" will also vary over time since the prices are all over the place, but that's the other advantage of not-ASICs. You can switch to whichever one pays better this month.

Sure, but they are so rare at present thay in my entire life I have not even seen one.