Claiming that national currencies are "backed" by the state is one of the more popular economic fallacies. Currencies work due to the network effect, not due to "backing". If the parameters of the network negatively change (e.g. the critical mass increases or people leave because there is a sufficiently good substitute), the currency will collapse. No amount of "backing" by the state can avert that. The maximum it can do is to attempt to prevent people from leaving, but that might not be enough. All the countries that suffered from currency collapses had armies. North Korea and Russia rank at place 4 and 5 of active military personnel in the world, for example (and Soviet Union was probably even higher).
On the other hand, situations where only the state collapses do not lead to dramatic changes in the use of currency. In Somalia and Iraq, people continued using the local currency even after the collapse of the state. At best they amend their activities with foreign currencies (e.g. neighbouring countries or the currencies with the largest markets, such as the USD and EUR).
Both of these are consistent with the use of network effect as an explanation: currency collapsing does not correlate with the power of the state, but with the empirical features of the currency (e.g. hyperinflation).
This is not specific to currencies. Plenty of other things work like this as well, such as languages, operating systems, the internet or operating systems.
Bitcoin provides a system with lower transaction costs and a predictable inelastic supply, compared to our current system that combines a monetary base and other forms of money, whether they are created by the state or commercially. Transaction costs provide a reason to switch. Of course, there's still the network effect, which hinders migration. The BitInstant Debit Card is a type of a multi-homing solution, i.e. something that provides a way of bridging the two networks. This decreases the critical mass for the Bitcoin network.