Proof of waste is an interesting way of putting it. I don't disagree. Maybe it would be interesting for power companies and govt to pair up and provide coins that are deflationary, and are only mined by putting power back into the grid. Make those coins useful to pay for car registration, taxes, or whatever. At least some deflationary value could be put to work there.
> Maybe it would be interesting for power companies and govt to pair up and provide coins that [...] are only mined by putting power back into the grid.
That idea sounds good, but would only be a solution for a problem that doesn't exist.
Bitcoin's design solves two problems:
(1) only someone who owns a coin should be able to spend it
(2) they should only be able to spend it once
The first problem had been solved for ages: use digital signatures to authenticate messages of essentially the form "I, Alice, hereby send 3 bitcoins to Bob." Given some initial coin assignment to specific private/public key pairs, you can follow along these messages, keep a tally in a ledger, and know how much everyone has.
Solving the second problem is where bitcoin innovates. Without a trusted third party coordinating things, Alice could just show a message to Bob and Charles each 'sending' them the same 3 bitcoins. Bitcoin uses proof-of-work to pick (at most) one of these messages to be part of the consensus reality.
The scheme you are suggesting requires some trust in the partnership of government and power companies. But as soon as you have very minimal amounts of trust, you can just solve the double-spending problem directly.
And that direct solution involves much less trust than what is required for accepting any statements about the power grid.
If you want, I can sketch out a minimum trust system for the direct solution I mentioned.
