The utility of the US dollar as being used as a currency is backed by the US gov't, but not the value of the currency.  What is the use of being able to legally spend the USD if it isn't worth anything?   People discount the effect of inflation on their money, and especially the possible hypter-inflation. 

And of course BTC doesn't need to be backed by anyone to be used, although certainly it may get to the point where it is illegal to transact with it.  That will slow it down of course but won't stop it.