I think it a yes. The government may shut down Bitcoin’s presence (in the same country controlled by that government) so that it becomes “basically non-existent”. The government may simply say that the mining of the Bitcoin; and/or buying/selling of the Bitcoin for the national currency; or some other services; or even the promotion of the Bitcoin or products based upon it is illegal – and punishable by a fine and/or XY months or years in prison.
When this happens, the activities overwhelmingly stop – just like the trading of hashish on the streets has stopped. Hashish may still be sold by the organized criminals in some underworld and that could still be the case of the Bitcoin. But the huge valuation of the Bitcoin we experience – and it kept on growing – is only justifiable by a mass adoption, by its being legal enough. Most of the speculators are arguably law-abiding citizens outside the cryptocurrency activities. They don’t sell hashish because they know that someone could find the evidence of this wrongdoing in some way and exactly the same could be true for the Bitcoin trading or mining or other activities (ISPs could be forced to monitor a suspect, and so on).
The Bitcoin is a global phenomenon and governments only control countries. So the bans in a country may affect all the users in that country but they may fail to affect the Bitcoin users in the rest of the world.
In this sense, the ban on mining in China would be rather crippling for the Bitcoin because 2/3 of miners are located in mainland China. China (which so far only banned the ICOs and exchanges operating in China) could also confiscate the miners’ hardware and organize a 51% attack against the Bitcoin or anything of this type – undo transactions or force a change of the Bitcoin rules on the network. In a very tangible sense, China’s government – not quite a democratic one – really owns the Bitcoin network and everything in it, according to the rules defined by Satoshi Nakamoto. The whole idea is based on the majority of miners’ control over the validation of transactions and China – and therefore the Chinese government – basically has this control. This is what Nakamoto’s paper unavoidably implies in combination with the Chinese government’s ability to outlaw or confiscate this hardware.
When it comes to the holders of the capital, the existing Bitcoins, it’s an entirely different geographic story. Most of the coins are owned by the Americans. So a U.S. government ban that affects the holders would be crippling for the Bitcoin. If all the law-abiding American owners of the Bitcoin were pushed to sell, the price would surely go very close to zero because of this huge oversupply. It’s questionable whether the price could significantly recover – because of buyers in other countries – after such a catastrophic decline. I think it would be extremely risky to jump on that bandwagon again because the Bitcoin could even more easily be banned in the “most important surviving country” after the U.S. and other countries, too.
The idea that the government cannot control the Bitcoin is one of these amazingly ludicrous parts of the propaganda that is driving the ongoing mania. It is extremely trivial for governments to shut down the Bitcoin usage. They haven’t done it so far mainly because it seems like a relatively small, innocent activity that only produces limited tax evasion and the users take the responsibility for their huge financial risk. It doesn’t tangibly hurt or threaten anybody which is why no government has cared too much. But it’s arguably changing as the Bitcoin has grown by an order of magnitude in a year.
It’s also a myth that all the Bitcoin wallets are anonymous. In reality, most people trade through Bitcoin exchanges and all the U.S. users above a certain value of holdings have to reveal their identity. The U.K. is introducing even harsher measures against money laundering and it’s similar in other countries. The FBI almost certainly knows the identity of a vast majority of big players in the Bitcoin blockchain, too. The idea that one is “actually” remaining anonymous when he does big things with the Bitcoin is a fairy-tale. On top of that, the investigators may simply demand the user to reveal all the information they need. They may point their guns at the suspect’s head. The safety of cryptographic methods is too weak and irrelevant a player to compete with actual investigators and law enforcement officials. Our society is still run by the people and the Bitcoin users are humans, too. Some some technological details about a cryptographic system simply aren’t important in the society.
Aside from outright bans, the governments may try to regulate the Bitcoin so that it follows the same rules as analogous institutions based on the national currencies. In this sense, the emerging wise U.S. government and even Chinese government attitude is that the miners are basically banks – trying to play the role of central banks, in fact. Bitcoin exchanges are like commercial banks or platforms to trade securities or commodities. So the miners and exchanges should be sure to obey some regulations that other banks with the U.S. dollars should obey. They have to have tools against money laundering, tax evasion, identify the clients when ordered, and lots of other things. Almost everyone who has made profits in the Bitcoin failed to pay his taxes. Once these people start to be prosecuted just like other tax evaders, this may be enough for a fire sale and the death of the Bitcoin.
Note that the current total price of Bitcoins is almost $200 billion and almost all of it is “someone’s profit” because almost all the owners bought at a much lower price. So it’s some $100+ billion in profits and tens of billions of dollars should have been paid in taxes for capital gains. Almost no one has paid a penny. So it’s clear that this phenomenon is becoming a big enough fish in tax evasion that the governments shouldn’t ignore anymore.