It makes sense to me, since in principle the amount of currency in circulation could naturally adjust to the size of the economy. To make that work maybe you'd need demurrage, to prevent utilities from printing up kilowatt vouchers for production in the distant future.
Since a watt is a watt, you could have as many issuers as energy producers, without worrying about exchange rates, though limitations of the electric grid might force them to be somewhat local.
You wouldn't purchase my heating bills from me...
Exactly, technology improvements can and do change the energy used.