This can't work because it just raises the efficiency of mining. That means mining will become cheaper. That means your reward is higher. That means you can mine more for the same money. That means every miner does that, increasing the part of the heat that's wasted.
In the end, the exact same amount will be 'wasted' as before.
Consumers that are already using (electric) space heaters are already paying $X/mo in electricity.
If they are getting value out of a bitcoin-mining space heater, it is justified to run at any time you want heat, because by getting a BTC rebate of any amount would make it cheaper to run than a space heater.
If enough miners are mining for the purpose of heat, it will push non-heat miners out of the market, because the heat-miners are rationally willing to mine at any price (any 'rebate' on expected electricity->heat costs is useful), whereas the non-heat miners can only rationally mine when btc reward exceeds electricity cost.
(We are a LOOONG way from the majority of miners using the heat, but just wanted to point out there is a hypothetical future where the market could eliminate heat-wasted mining)
ActivityPub can be used in a P2P situation. The biggest problem for that right now is that we use DNS for finding other instances, so you will need something with a domain name.
