Burning US $1 notes could not provide backing for minted coins. A better analogy is currency backed with gold without enough in reserve to handle a run on the bank.
How does burning over 100 MWh of electricity provide backing for a minted coin, yet directly burning currency doesn't?
What's the difference, besides the pollution?
It could provide some level of scarcity, so if there was demand you could achieve some sort of value. It wouldn't be stable though - you couldn't make a stablecoin on proof of work either AFAIK. I guess it'd have an upper bound at $1 (why buy it for $2 if you can just burn $1), but no lower bound. So.. maybe it is a stablecoin :)