Bitcoin opens many doors of new markets, which would affect the economy of a country, the reason why there are some countries who don't like bitcoin because cryptocurrency controlled by no one and because they don't get taxes. But if governments open there eyes and use bitcoin in its positive ways as possible you would be shocked that the third world countries who opens their gates on bitcoin will become one of the best countries we have ever seen.
No, I do not think that the importance of bitcoin in the current economy is as great as OP thinks, because its market and its level of acceptance is still too small to influence in such a remarkable way in the current economy. I think it is still a long time before the cryptocurrency market can dramatically influence the global economy, and when the conditions are right for that to happen, bitcoin will have to face a great competition of new and more advanced cryptocurrencies that threaten to gradually displace bitcoin from its current hegemonic place.
Earlier all the monetary transactions were enabled through central banks (directly or indirectly). Now, with the evolution of Bitcoins, the scenario has changed. The power that was vested in the governments and central banks is shifting to the masses.