Bitcoin is backed by the cost of electricity (and equipment) required to compute its proof of work.
Not correct, though people say this very often.
"Backing" when talking about a currency has a very specific, important meaning. It means that some party has promised to redeem that currency for some other good of value. Backing requires a backer, in other words. It requires someone's promise to back Item A with Item B. This is how paper money can have real value, because if it's backed by a government or bank or corp that will give you gold/silver for it, then it has that same value by proxy. That's backing.
Bitcoin is not backed by anything, nor anyone. It is a resource, a commodity, a good in and of itself.
The cost of electricity/equipment does not back Bitcoin whatsoever, just as the cost of dredging deep-sea mud from the ocean floor doesn't back the price of this mud on the open market.
I agree. Governments back currency to create confidence.
Bitcoin derives confidence from being useful as a currency. The ultimate currency should be easy to use (make micro-transactions simple and close to free), be secure (from fraud, government seizure, and provide anonymity), and be a good store of value (scarce). To the extent that bitcoin scales to these tasks, is the extent that bitcoin will prevail in the long-run.