Gridcoin: An open-source cryptocurrency that rewards volunteer computing
This may be misunderstanding the function of PoW. Bitcoin PoW provides three things: selection, security, and incentive. The compute resource burn is an externality, although, it also ends up providing an important function, economic distribution. For PoW to work,it has to be hard to produce, easy to verify, and most importantly, attest to one and only one state of the blockchain. The last part is where this fails as PoW. The solution to a puzzle is meaningless if the same solution can be shown as the result of two different inputs. So the puzzle must be practically unique to each proposed block (infinite possibilities), and ‘fair’ to each proposal. If you can find a useful puzzle with these properties, please don’t hold back.