First of all, I'd like to say that I completly agree with what JackNZero236 said. But, moving on, as much as I think it could be nice --if not complete global domination but at least world peace -- I don't think it would ever happen. Everyone has the right to their own opinion, and this is mine. You don't have to like my opinion, but I ask you to respect it, as I do yours.
I think it would be too too hard. To get a strong country, you need internal and external peace. Obviously, if there was only one country, we wouldn't need to worry about external problems, but, internally, we'd probably be a mess. One of the things I love about our world, is that we have a multitude of opinions, cultures, and views, and this, in my opinion, could be the downfall of the Country. Firstly, within the country, we'd be throwing cultures and peoples together that have hated each other since the start. Let alone having one civil war (such as the American Civil War), we'd be having multiple civil wars going on (Palestinians vs Isrealis, Sunnis vs Shiites...just to name a few). The Military would be streched too thin to keep the Country unified. Secondly, the Government would not be able to please everyone. Think of America, and all the problems we have. No matter what our government tries to do, there is always someone complaining about it. That is with moderate sized country. Now, with the Country, with all the cultures and peoples, it would be even more difficult, if not impossible, to please all the people in the Country. Rebellion would happen, and soon enough, we'd be back at square one, with tons of countries. This would then be hard because we would have hundreds of "baby countries" (if you don't mind the metaphor) trying to learn how to walk.
Don't get me wrong, the Greeks and the Romans were great. But that was then and this is now. Their "world" to conquer was much smaller than our world now. They had less people to worry about, less to please. Even if the Government wanted to take the example of Alexander the Great (adopting some of the customs of the countries he conquered), it would be too much of a strech with so many cultures and only one Government.