Dave, I agree that humans are, and have been, our worst enemy for a long time, now.
Unfortunately, it seems to be embedded in our nature. So, I don't think that "a global government with true power" is going to provide the solution. Because, without human nature itself changing, that government is likely to become controlled by corrupt people who use it for personal advantage or ego, at the expense of the governed. We have seen that in history, and we can see it operatiing today in several current dictatorships.
So, it isn't the centralization of power that humans need to learn, it is the need for cooperation for the benefit of others in order to best benefit ourselves. And that is not just the benefit of human "others", but the benefit of the whole ecosystem that we and everything else alive on Earth actually need to survive and thrive.
There are physical limits, and we must learn to live within them as a species. So far, we keep getting into fights over who gets a bigger share.
IF we can learn to overcome that, then it is that change that might provide for one common goverrnment to be beneficial from an efficiency standpoint. But, the way we are now, we really need multiple options for governments, to reliably avoid a whole-world dictator.