This is only true if the value of the Bitcoin you mine is higher than the difference in cost between buying and operating a heat pump and buying and operating a mining rig.
I don't agree with a lot of things in CAPEX vs OPEX, but this is one that is clearly right:
Having equipment sitting around unused is way more expensive than most people care to think about.
A heating coil might not be terribly valuable in July, but come November it will have roughly the same value it had the previous February. Bitcoin mining hardware that's switched off for five months is losing value at an alarming rate, and very quickly won't be a net reduction in costs.
Very quickly a heat pump becomes cheaper to operate, and cheaper to purchase. And if you amortize the cost over the life expectancy, that threshold is very, very low. People who have recent memory of living paycheck to paycheck are constantly screwed by the latter, and that Venn diagram overlaps heavily with several other circles that make crypto super attractive to some people and super ridiculous to others.
I went down this avenue of compute as radiator long ago, and I could never get the math to work, unless I moved somewhere that was cold most of the year, and that sure as fuck is not going to happen.
In a very brief nutshell, the ways in which buying a little hardware or a tool to save thousands of hours of frustrating development work is not a slam dunk because of colors of money.
In either case, you still have to compare against using the fossil fuels to heat your house instead of turning them to electricity first, to heat your house via the heat pump or the resistive heater
In that case you would still have an absorption refrigerator that "cools" the outside and dumps to the inside as an alternative. They are usually either gas-fired or running off of district heating (well, 50-120C seems usual).
2/3rds of that cost is labor. 3 ton multi-zone heatpump kit is $2500-3500, another $250-500 for an electrician to pull #6s and a ground to a 60A disconnect outside and sealtite whip into the heatpump, and 60-80 hrs at $125/hr to install the heat pump and air handlers, including all the exterior wall penetrations and sealing, running glycol lines, installing thermostats, wiring air handlers, etc.
Yeah single room. There's dual room splits that run a bigger compressor with two heads too. They are usually way cheaper than bigger units even when you account how much juice they eat up but you should do your own math because it depends on the house and the setup.
Also if you want to control every single room including bathrooms and walk in closets it gets tricky.