In winter if one uses resistive electrical heating and where heat pumps are not allowed like in some apartment blocks mining can be free as the consumed electricity just heats the home.

You would be better off spending your money on an air or ground source heat pump though...

I live in an apartment in Norway where an air heat pump is not allowed by regulations and the ground source is way too expensive even with the current electricity prices and will take years to get approval as the area is considered a historic part of the town and must be preserved.

So couple of years ago I permitted for my son to mine coins on GPU when it was cold allowing to him to earn like 2-4 Euros per day.

But then I stopped as I realized that this just promoted insanity of using proof of work in other places.

Wouldn’t an electric space heater provide more heat per watt? This isn’t a rhetorical question because I don’t know the answer. It’s just my intuition that something designed to produce heat would do that more efficiently than something designed to do computations that produces heat as a side effect.

Basically, heat is waste. A space heater is a resistor causing 0% efficient usage.

If 500 watts of electricity go into a heater or a computer, 500 watts of heat will come out, minus some light from leds and screen, some electricity on the ethernet cable, and other of these ignorable things.

If it does some usefull computation on the side, that's nice, but energy wise a 500 watt game computer is just as efficient as a 500 watt heater, if used for heating purposes.

No it's same thing. All energy eventually becomes heat and there can be no lost energy in a system. In the case of a GPU we're converting electrical energy into thermal energy, and some mechanical and sound energy due to the fans. So a GPU should just as efficient at producing heat as a space heater, it's just that the electricity goes through a few more steps first.

Of course, but what he's saying is that you don't generate currency as a side effect of running your dedicated heater. Whereas the inverse is true with mining - you generate heat as a side effect of running your mining setup. When that's desirable, it can be factored into the net cost.

If home power generation was cheaper (considering all costs) than grid generation, everybody would have a home setup.

If you have excess capacity and no way to sell it to a grid, then it might make sense to do some mining, but then you are really just recouping some of what you over spent on solar panels.