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).
Just take a look at your own country, at the constitutional founding of the country the population was about 1/100 of the contemporary size and yet the political system has remained basically unchanged. Despite this massive population increase it is a well-functioning democracy. There are of course anti-democratic forces but they have little to do with the population size of the country and more with a concentration of wealth and power.
About distant elites, if you take a look at the Civil War and the Civil Rights movement it becomes obvious that it was the central government which fought against slavery and discrimination.
Nothing of this is particularly surprising, human values are universal (you can play the postmodern game but I am not willing to excuse something like genital mutilation with "culture" or "local values") so only a universal government can enforce them. Last time I checked we also try to move into this direction in the real world, international law, holding leaders who slaughter their own population accountable and so on.