That's a strawman I'm afraid, the real question is the relative energy per-transaction costs between Bitcoin and traditional currencies. Bitcoin just doesn't scale.
17.7M barrels of oil annually by bitcoin mining operations
8.16B barrels of oil by US banking sector employees
These numbers don't count the physical infrastructure, servers, and other plant that these businesses own, operate, heat, keep the lights on in.
Here are my sources:
One stat I just read says that the top 20 North American banks employ 1.2 million people. That's 1.2M people eating and commuting 5 days a week for the purpose of supporting fiat.
With a quick investigation:
-US per capita annual barrels of oil: 6800 (1)
-Bitcoin annual Terrawatt hours: 30.1 (2)
-6800 * 1.2M = 8.16B barrels of oil by US banking sector employees (3)
1: https://www.statista.com/statistics/250220/ranking-of-united...
2: http://www.wired.co.uk/article/how-much-energy-does-bitcoin-...
3: http://www.kylesconverter.com/energy,-work,-and-heat/terawat...
They aren't really "supporting fiat" as you say, they do things that (presumably) have value like storing money, making loans and...whatever else it is that banks do.
If all the world's central banks decided tomorrow to stop the printing presses banks would still have a function in society independent of "supporting fiat" as they have had for a long time.
- Energy required to harvest and process hard currency - Energy required to run the servers that support electronic transactions for fiat
Then divide that by the overall value of fiat vs bitcoin to see how costly they are per unit of value