Technically it is backed by guns, guns that convince other nations to trade in USD and guns that convince US citizens to pay taxes so that the guns are pointed at those who don't pay them.

The other factor is that the US has adopted the USD. The actual reason (e.g. guns) doesn't matter, it only matters that the decision has been made. You can buy things in the US with USD. Therefore the value of the USD is tied to how much stuff a dollar buys you.

The size of the Bitcoin economy is quite small. There are not many things whose price is denominated in Bitcoin, most shops just convert from the dollar price to Bitcoin, which means there is barely any price stickiness that keeps the value of Bitcoin stable. If anything it supports the instability of the exchange rate.

/dev/null

Are you talking about the Dollar?

Gotta hold dollars to pay US taxes. Don't need to hold Bitcoin to do anything at all.