Just wanted to make the point that transaction cost isn't measured in kWh, it's measured in plain kW since there is a finite amount of time it takes a transaction to be mined.
This is the exact reason why it is measured in kWh (energy) and not kW (power).
It takes an amount of Energy to mine a block, not Power. Power is not descriptive as you could have 1kW running for 10 minutes or 10kW running for 1 minute and you would have the same result.
How could Power (kW) be used to measure the transaction fee? Could you explain what you meant?