Bitcoin, at least, absolutely does not solve this problem. Let's leave aside its volatility for now and assume it magically stays at exactly the same price. You are then left using a currency where each transaction costs several dollars and takes a half an hour, and that's the present state of affairs when no one is using it. So you would keep your cryptocurrency in a bank and transfer it through the normal channels, which opens it up to the same government controls you're concerned about. That's if you're allowed to hold cryptocurrency at all.
Hyperinflation is a problem of massive corruption and incompetence in government. It doesn't happen by accident in an otherwise stable society. If you're concerned about hyperinflation, you should assume the bank (or "exchange") will be subverted and transactions will be censored. Bitcoin was built to solve those problems, but does not scale and so cannot.
This is, by the way, the only situation where I'm at all sympathetic to cryptocurrencies. If someone can come up with a cryptocurrency that scales and that isn't controlled by cartels, I'll be glad that it can be used in unstable parts of the world.