So, money can't be separated from the state? That's another topic, though.
Is it possible to use a new breed of fiat, centralized money that's issued by banks but backed by Bitcoin? But I'm not sold to the idea of fractional reserve. It should be backed 1:1. The only reason banks issue another currency is convenience. Fractional reserve, to me, is the new monetary system's road to perdition. But I remember even Hal Finney predicted fractional reserve Bitcoin banking. Perhaps I just don't understand how fractional banking properly works with Bitcoin.
Backing Fiat with Bitcoin has been an idea proposed by some governments for a while now. But for many economic experts, this would become an impossibility. Because there are only 21m BTC in existence, while Fiat's supply is much larger. For instance, the US has a $36T national debt, which greatly surpasses the current market cap of Bitcoin. Backing the USD completely with BTC seems nothing but impossible.
Instead of backing Fiat with BTC, the ideal solution would be to replace Fiat entirely with BTC. Like people relying on Bitcoin as a standard unit of account. But again, governments will never allow this to happen. At least, it's better to have something than nothing.