No bitcoin can not become a global currency the governments around the world would never agree to it. For there to be one currency there must be unity all around like the European Union but there is no such thing in case of whole word and nor it is possible in future to have one world without countries.
Have you read
franky1 reply? Bitcoin being on the internet automatically make it a global currency, the only problem that lies is the question, will government acknowledge it? Well, some did some did not and majority are on stand by waiting for development country to deal with cryptocurrency and will follow their lead.
I think being global currency does not mean dominating the world and be the only currency used by all. See USD, it is a global currency and yet there are still many other currency existing in the world.
The main reason is all bankers are against bitcoin due to decentralized system.
Not all bankers are against Bitcoin, look at Japan, since the government are into cryptocurrency, banks in Japan welcome it with open arms, Some of the banks here in the Philippines are crypto friendly too.