Using US dollar as an example of a fiat currency, as backed by its military etc. is a bit disingenuous. It has been steadily losing its value against Swiss Frank over the years. The whole of Switzerland, last year, used 58 TWh, which is half that of Bitcoin. Its military expenditure is 5 billion a year, compared to 934 Billion of the US. Clearly, the value of a fiat currency has relatively little to do with the military of the country backing it.
If you are looking at the energy budget of fiat currency, you inevitably have to also look at the energy budget of a transaction of fiat currency.
What is a fiat currency transaction? For example, you tossing a coin to the homeless person on the street, or paying for a beer at the kiosk. Something that happens hundreds of thousands of times per second world-wide, vs. Bitcoin’s maximum of 7.
Now, the fiat currency transactions get cheaper every day. Banks are closing shops. Not because of crypto, but because a lot of those transactions already happen electronically. That is just as true in Switzerland, as it is in Kenya. (By the way, M-Pesa, the cellphone banking system in Africa, has about as many active customers as Bitcoin.) With traditional electronic banking, one server can process thousands of transactions per second.
Running an AWS web server gives you a good estimate of the total cost of a transaction, because Amazon charges you for everything, including hosting, security, lights, etc. You’ll find, it is not a lot. It certainly isn’t the price equivalent of 550 KWh for a single served website. A cost/energy budget of a few HTTP requests is what a cost of one electronic monetary transaction should be. I am sure you can see why that doesn’t work with Bitcoin (or any other distributed ledger, for that matter.)
The main reason traditional banking is slow, or expensive, is mainly because it is heavily regulated, and the regulation is often 200 years old; some places because they were early adopters and invested heavily, and the infrastructure is written off over 30 years, etc. This is changing all over the world. If the banks have to actually compete with each other in terms of service or price, they will sooner or later figure out how to save money, and thus, energy.
The transaction energy budget of Bitcoin however, will not improve. The block is meant to be generated every 10 minutes. The more miners join, ie, the higher the hash rate, the lower the target, the more attempts (globally) it takes to find a matching hash, the more energy it will use. It is built that way.
And one more thing. If you are looking at the world’s fiat currency system, you are looking at something used by a good portion of 7.5 billion people. If everyone opened a bitcoin wallet today, and some cryptowhale gave each one of them a free satoshi for his trouble, it would take 30 years for all the transactions to process. As you can imagine, under these conditions Bitcoin is never going to replace the fiat system world-wide, not even a significant portion of it — it is simply technologically incapable of that. This is why you can’t compare it to the fiat system, especially not favorably. And if a crypto system one day does replace fiat cash, do you think people would magically not have to pay security to guard their mining farms?