Them not being directly controlled by governments doesn't mean that they exist in a vacuum. At the end of the day, it's people creating/buying/selling them, so obviously they're affected by: governments, natural disasters, wars, ...
Or Batman dressing like a bat because "criminals are a superstitious and cowardly lot."
Bitcoin will survive for the simple fact that as long as something somewhere is illegal, Bitcoin will have value.
Monero, for example, uses ring signatures to enable a greater degree of anonymity by having x% of block transactions be complete gobbledygook. Sending someone a transaction doesn't unmask your transaction activity for them to see (unlike Bitcoin), values transmitted are obscured to people browsing the blockchain (unlike Bitcoin), etc.
Bitcoin isn't the best, or even a particularly good cryptocurrency for engaging in extra-legal activities.
This has so many meanings that you can be both right and wrong at the same time.
What I haven't been able to get a straight answer on is exactly which specific types of power. Because as far as I can tell, a government could still levy taxes in BTC. They could still impose whatever financial regulations they wanted on top of BTC. They couldn't force or prevent transactions, but they could still observe them and impose fines (and, ultimately, jail time or asset seizure) on entities who didn't follow the regulations. They could still demand record keeping and reporting from any businesses they wanted, and would still be able to perform audits to ensure compliance. Given that most of the blockchain implementations allow a third party to easily reconstruct transaction histories, quite a few types of regulation seem like they would actually be easier to enforce.
As far as I can tell, the only governmental function that cryptocurrencies actually disallow is central banking. That may or may not be a good thing, but either way it doesn't feel to me like a world shaking reclaiming of some fundamental liberty from the clutching tentacles of the Leviathan, and it doesn't seem like it would fundamentally alter the day-to-day experience of participating in the economy.
So, what am I missing? What should "not controlled by the government" actually imply, specifically? Or, if that's the wrong way to express the underlying sentiment, what would be a correct statement of the idea?