They can do that because they are the US govt.
What would be the likely consequences of the ban?
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Same as the ban on drugs:
Or the similar example with drugs but with another consequences in Saudi
I can not say that they banned it, because they were illegal all the time. But because the price for breaking the rule is so high (Death) almost no one tries to possess or sell them. Moreover, if anyone would find out that you have them, they would tell about you and this will be the end for you. I can not say that in this case the government is spending a lot of money, their try is very efficient and for sure they are far away from failing.
If someone think that this is not the case - try to go there and try to buy some :-). Before this - just send me your bitcoins, I will for sure give them back if you will come back. This was a joke - I am not promoting drug users here.
In the end - all depends on regulations and how will it be enforced.
The USA is only one country of many. Others will continue to use bitcoins.