Part of the promise of Bitcoin is that it will eventually force governments to reform their own systems simply by presenting a better alternative to people. In order to compete and retain some semblance of power, governments will have to address the market conditions and become serious about reform, if only for the sake of self-preservation. If things were really looking like all fiat was going to go over the cliff of hyperinflation due to wealth pouring into alternatives, then they would have no choice but to engage in serious reform. Any such reform will help to stabilize national currencies and make them attractive enough to stem the tide of the nightmare scenario described by the OP. People will have time to adjust.