The dollar bill is worth 1 USD because the government asserts that.
That doesn't make 1 USD anything. It just means the dollar bill is worth 1 USD.
The government has no power to prop up the value of the USD if the world decides it's worthless.
I don't see "the world" deciding USD is worthless anytime soon: people in third world nations keep pristine US cash in their closets as a store of value; a lot of international trade uses dollars as a common currency; etc. If "the world" decides that dollars are worthless, that will be the least of my problems while I'm cowering in the bomb shelter I don't have.
Same for BTC.
The US government has plenty of military power that it can and does use for this exact reason.