The economics of bitcoin mining dictate that the work must have no other utility. If you increase its profitability by using it for auxiliary winter heating, then more people will mine bitcoin until there is an oversupply of heating and we return to the current equilibrium amount of "wasted" heat.

This seems to indicate a serious misunderstanding of both bitcoin's economics as well as the feasibility of having an "oversupply of heating". Hundreds of millions to over a billion people globally lack reliable energy for lighting, heating, and cooking. And bitcoin's economics don't dictate that mining never have a side benefit.