Fiat currencies will still exist. Remember, Bitcoin is a competing asset to fiat, not a wholesale replacement. I suspect that even if central banks adopt Bitcoin as a currency reserve, their fiat will be pegged to it by some ratio only.

At some point, the real yield on a government treasury will exceed the real yield on Bitcoin, indicating that a better savings rate in fiat is available. This will shift value back out to fiat, similarly to the way gold inflows/outflows in expansion and recession.