Overall, this debate is way too general, however depending on different circumstances, there are different problems that may arise. I understand that this isn't a real debate. One obvious problem is the lack of compatibility between different regions and forms of government. Virtually any religious country would not tolerate a totalitarian government, at least not for long. Muslims in the middle east would not be for a world democracy. The world is in general more Christian than Muslim, especially when comparing those not only that are Christian and Muslim, but have Christian culture and Islamic culture. Those of Islamic culture would not want their rules being made by Christians, not only because of resentment between the two groups, but also because there are certain Islamic beliefs that do not work with western democracy, a prime example being women's rights. A republic like the United States would not work well either. This is because there are massive income gaps between nations. Therefore if each nation acted as a province, nations like the U.S. and Germany would face much higher federal taxes than places like Zimbabwe or Macedonia. It would not be beneficial for the richer states to be a part of the global union. I don't see a situation in which it isn't beneficial to every single nation of the world to join together to form one nation. It would also face similar problems to the Roman Empire. The Romans allowed different areas of the Empire to maintain their own cultures. Those different cultures created a lack of Roman identity in the long run. This lack of identity made the people feel more loyal to their local area than the Roman Empire, which allowed rebellions, new factions to form, and the eventual fall of Rome. There are far more differences across the whole world, and those differences are more potent.
Overall, the arrangement would fail because of a lack of a loyalty due to existing cultural identities, and the lack of benefit to all member nations.