Dream big. First, assume that crypto isn't suppressed by force - monopoly of force is broken, at least temporarily. Then what happens if crypto wins? Fiat starts failing, but then...
...people will still demand "centralized government services" of some sort. How do you account for those?
Solution A: Private markets entirely trading in decentralized crypto.
Solution B: Government operates in crypto balances.
Sol. A eventually resembles Sol. B when a single party gets big enough. Either way, once you have a big actor, the incentive to take control of currency again rises anew - write out debt, impose market controls, etc. Thus we get a govcoin as Solution C: Centralized, uses strong identity, cuts the majority of today's bureaucracy. It can be 99%+ digital with paper as an "emergencies only" backup. This means...
...the economy can be tuned in ways unavailable to both fiat and decentralized systems. "Money supply" is a crude tool for managing transaction flow - it's abolished in favor of a pastiche of sinks, generators, taxations, records, rules and rewards as seen in online digital games. It can play sort of like capitalism, but with increasingly little drudgery exposed to humans, and made more efficient and motivating besides. I would note that there are already exchanges between game assets and crypto - the games are good enough to make people sit there clicking for hours, they need only be repurposed and scaled up to animate the larger economy. The only limit to their specific design is your imagination.
But how do people end up preferring the new govcoin over crypto if they start in crypto? Through the same mechanisms as the "free" model of today's popular online services. The coin and the associated rights and services are issued to you in exchange for your identity. Proven, well-understood marketing mechanism; may be done without your consent, via the existing institutions that track you. And as long as the government works for you, you play within its rules, no matter how arbitrary. When it starts failing, you go back to crypto, just like how older economies cycled between gold and fiat.
Recall that we are assuming monopoly on force is broken. But force is likely to be increasingly accessible to individuals in the future; if they don't already have a weapon, they will have tools that can make one. So the monopoly that will matter is monopoly of information - finding out who is dangerous. Governments will assume the worst of someone who isn't within their systems and subject to monitoring, so they will, sooner or later, start pressuring people to enroll. This doesn't, however, stop people from being a non-participant in the economic game the government is providing. The old tensions will continue to exist, but the mechanism to signal loss of faith will be through speculation on crypto assets. Governments will start moving at the speed of technology, because they will have to - if they want to be competitive.
So as I see it, govcoin is in all facets anticipated by existing systems and technologies; crypto is the mechanism that motivates its reification as a concept worthy of discussion. The two are already in competition with each other, but crypto is surging ahead right now, as we still discuss both in the dying language of industrial capitalism.