I'd be wary of the Star Trek
future in which the whole Earth falls under one government. It's apparently a prerequisite for us to found the Federation, in which every planet counts as one member (but we're the big dog and don't forget it
). Even so, it has disadvantages.
A single government for the Earth would have so many citizens that it simply could not be responsive to them. We'd be ruled by distant elites who would not necessarily share our values and priorities (much like the European Union today, in the eyes of many of its people).
And those elites wouldn't need to be responsive. A government with six billion constituents would not have to answer to any of them. Assuming you even had an elected representative in the legislature, he would either be powerless because the legislature is so large, or he would have so many constituents that you would mean nothing to him.