A world ruled by one government would be an authoritarian dystopia

Herding Cats: The Final Frontier

The record of history is clear: as the population of a nation or empire increases, its government becomes more authoritarian. The Roman Republic became the Roman Empire when its population peaked. The same goes for the transition of the Russian Empire to the Soviet Union, and of the Qing Dynasty to The People's Republic of China. 

The larger a society is and the more diverse it is, the greater the amount of violence the government must use to maintain a monopoly on force. This was discussed in The Federalist Papers. States expand through force and very little else. 

Given that, it follows that a government with no competitors could focus all its energy on oppressing its subjects. And it would be efficient in meting out violence because it could have only become the sole government by conquering and absorbing all the others. 

The whole world would be like North Korea, except there would be nowhere on earth to escape to. 

For these reasons, I am opposed to organizations like the UN, NATO, and the EU, among others. Diplomacy works best when the number of negotiating parties is kept to a minimum. 

Of the 10 freest countries in the world, the one with the largest population, Sweden, has only 9 million people. This represents a bit more than 1% of the world's population.

The only example of a large society with a high degree of freedom is the US, and the reason for that is individual freedom is baked into American culture and laws. Countries with similarly large populations like Brazil, Nigeria, Pakistan, and Indonesia are all less free and less prosperous than the US. This is not judgement of their cultures, only of the results brought by their economic and political systems. 

Countries with very large populations like India and China are also less free, though India is much freer than China. 

In short, nationalism is good. Good fences make good neighbors. The idea of everyone living under the same government is as absurd as everybody living under the same roof.