But questions is, what problem are you trying to solve?
energy? You cant save energy when it is proof of work.
Lets assume, somehow we come to agree to make Bitcoin HARDER (you know, lets burn some fuel) to solve. Lets say, we will somehow make it 10 times harder to solve.
Do you know what will happen? Bitcoin network will just ADJUST itself back where it was. (10 minute mark) It does not MAKE ANY difference.
Perhaps I don't understand something, but I agree with Meitzi. According to the design of Bitcoin's PoW, the average cost of mining a block approaches the average value of the block reward. That is why more a efficient hardware (in terms of J/hash) does not change energy consumption. How does your scheme change this design?
This is my understanding as well. A different way to put it: if all miners get 10x more efficient, thus hashing with the same hashrate and 10x less energy, people will run 10x as many machines, the difficulty goes up 10x and
BTC consumes the same amount of energy.
This is not an issue of your proposal, but a general concept that can't really be circumvented when coins are minted using energy.