The US dollar is backed by the sovereignty of the US government, the ability of the US government to impose taxes, and their willingness to accept the US dollar in payment of all tax obligations.
If the Fed used the Bitcoin blockchain as the ledger to settle tax payments, then Bitcoin would be a currency and would have something backing it. However, this would create a horribly deflationary economy which would plunge the country into a period similar to the middle ages in Europe where coin scarcity crippled productivity.
> The US dollar is backed by the sovereignty of the US government
This is completely meaningless. You're just repeating something you heard. Anyone with a coherent understanding of the USD's value proposition would not describe it this way.
> their willingness to accept the US dollar in payment of all tax obligations
This is a real, but small, factor in the value of the USD.
> would plunge the country into a period similar to the middle ages in Europe where coin scarcity crippled productivity
This isn't an issue with Bitcoin. There's no "coin scarcity" due to its high divisibility and near-ideal fungibility.
If the Fed used the Bitcoin blockchain as the ledger to settle tax payments, then Bitcoin would be a currency and would have something backing it. However, this would create a horribly deflationary economy which would plunge the country into a period similar to the middle ages in Europe where coin scarcity crippled productivity.