I'm wondering this because is such a real threat to bank system and we all know how banks and governments are tightly linked !
BTC could make people more autonomous, self-resilient, being their own bank. You can use it like cash, making your transaction almost untraceable (or untraceable using e.g. monero or dash or laundry systems) : this is governments worst nightmare, isn't it ?
They can't!
The thing is the worst thing they can do is shut down exchanges, ban ICOs, whatever. But to shut down or ban bitcoin itself is just impossible. Sure, they could say on paper that bitcoin is illegal but people will continue to use it. Just like when in some countries where their currencies are extremely unstable people turn to using the US dollar even though it is officially banned(e.g. Zimbabwe).
If governments banned bitcoin, people are going to continue to use it. As it is a distributed ledger, governments can't just shut it down.
i think its fully possible for a government to shut down bitcoin entirely, it's just a matter of how much theyre willing to dedicate to the effort in terms of resources. iirc, law enforcement was able to pinpoint illegal TOR based sites (not that TOR is illegal itself, but sites such as drug exchanges, child porn, stuff of that nature) by tracking ip response times and other factors (it's been a while since i've read thsi, wish i remembered it more clearly). in addition, bitcoin has an inherent weakness to the dedication of excessive resources: the 51% attack. if a government was willing to actually dedicate the resources to set this up, they could effectively start reversing transactions and manipulating the network to their means, which could lead to the death of bitcoin. at this point, they wouldnt even need to outlaw it, they would control it.