Decentralization and knowledge about how it works may be the two main reasons why governments wouldn't be able to "shut it down". Just look at BitTorrent, an amazing decentralized, fast and unlimited technique to share files. Governments claim it's only used by pirates but they haven't managed to shut it down yet. They even fail to shut down a centralized website (thepiratebay).
Knowledge may be even more important, people must know why cryptocurrencies are better than fiat in order to accept it and keep using it even if governments try to ban it.
Yup, i do agree with you. until now biTtorrent is still operational and many were using it including me, LOL.
Cryptocurrency is way better than fiat money but sad to say cryptocurrency have no gold reserve behind it or any reserve that have value to backed cryptocurrency. It is purely virtual - meaning not existent. Only the investors and users gives value to the cryptocurrency. The more users supporting it, the greater its value.
Its being virtual makes it very difficult to shut down and a herculean task to catch someone using it.
Since 1970's fiat hasn't been backed by gold either but that hasn't affected it's price tho, it keeps losing value at a relatively steady speed. The reason to back something up by physical objects is to keep the value even if we loose all electricity or if the internet goes down or something like that. Imagine how that would affect a regular bank and it's easy to see why virtual centralized currency is unsafe.
However decentralization opens up for more possibilities, at least in theory. We could run a full node deep down in a bunker safe from nuclear bombs to keep cryptocurrencies working even after a nuclear war.
We could also send a full node to the moon and sync via satellite links and it would survive even if the entire earth is destroyed (which would also remove all the gold).
With above in mind I'd say cryptocurrencies are safer than physical objects as it would take so much to destroy it that we'd most likely destroy ourselves first.
"decentralization opens up for more possibilities" - I do agree to this. This is one the reason why bitcoin is so popular right now and as of now, no one can stop its bull run. :)