I can definitely see them at least trying to ban it. Some countries, China for example, have already tried numerous times. I guess it's even theoretically possible to see all the countries join hands in issuing an international ban or crippling restrictions on using it. Possibly using some crisis in order to push through a global mandate against using it.

But if they really wanted to avoid entanglements they could accomplish this indirectly by appealing to everyone's insecurities. They wouldn't even need to address it by banning Bitcoin directly but instead focus all their energy on introducing a "better alternative" and demonstrating how they think it addresses the problems being created by the aforementioned crisis. They would then top that off by putting a carrot on a stick by offering people a starting out stack of their new currency.

Many people love the idea of "free money" so I can see people falling all over themselves to adopt this currency over Bitcoin, thus preventing a need to overtly ban it. And if the new currency has no advertised restrictions all the better.

And of course, we wouldn't have any reason to distrust these hand-holding governments either.