Yes, and some currencies do lose value because the government and economies backing them have lost trust.

The demand for USD comes from people wanting to do business with one of the biggest economies in the world. The demand for Bitcoin comes from people wanting to make money by hoarding Bitcoins.

It could be different, but right now it is not and I'm not sure if Bitcoin (or any other cryptocoin) would survive a transition to become a currency or something else less like a pyramid scheme.