One government to rule them all would not work. This is because the top leaders would have to much control. It would be to easy for a few special interest groups to control the world and make everyone else a servant. The current system of multiple countries works much better.
Looking back in history we can see that government over extension leads to problems. I do believe it is safe to assume that these problems have merely disappeared since we've moved into the technology age. I do not believe it is possible for one government to control the world and I do not believe it would make the world a better place.
The World is too diverse and big to have one government. Large countires like Russia have problems with government because their country is too big, there are too many different time zones, so imagine how difficult it would be for the world to have one government. There are also too many different languages, and cultures for it to work. The United Nations is a prime example of a failure of a world governing body.
Having one government would not make the world a better place. It would create a monopoly over the governed people. It is good to have a variety of ruling systems so that we know what to compare ourselves to and how we can improve. One single government just leaves too much room for abuse.
No, I do not think that having one government would make the world a better place, because the world would be extremely corrupt. The government would only be involved with taking wealth from rich nations and giving it to poor nations. We would not even agree on whether democracy and capitalism are better than other societies.