The value of bitcoin lies in bitcoin. It is digital gold. When paper money first came about most people wouldn't touch the stuff. What value does ink on a piece of paper have? You would have to be insane to accept that instead of proper money.
A gun to your head is the only reason why paper is used. Obviously in a VOLUNTARY world, nobody would use it. Likewise nobody would use bitcoin, because it has no intrinsic value. Commodities (oil, gold, etc) in digital form would take over completely. A few years back, E-Gold (digital gold) grew wildly popular, it had millions of users before Govt shut it down. Absent Govt, you would see BILLIONS of people using some form of E-Gold/E-Oil, etc.
Bitcoin requires the existance of the State for it to thrive.