You do realize your spiel could be used to market any of the conquests of the past centuries - unite under MY banner, and we shall have piece...
Britain is pretty swell, after a thousand years of dominating cultural hegemony. Although some scots may disagree. And some Irish perhaps. Not too many people speak the old tongues.
A typical dynamic in a large polity such as a nation or a corporation is that there will be a single culturally distinguishable leading elite class, and a) this elite will favor it's own (not maliciously, but because they are human and favor familiarity) and b) the people who do not actively recent the ruling elite will try to emulate them. So, in time, if the dominion can remain civil, it will develop an understanding and a common cultural framework.
Talking of civility - historically, britain has been unable to hold to lands that it could not hold under the force of violence. American colonies. India. South Africa.
People love their sovereignty (or, people yearn for political power and use sovereignty as their rallying cry). Anyhow - if the cultural hegemony cannot overwhelm a territory there will be a constant pressure to cede. I think this understanding of history is what drove many of the genocides of the past century - political will to rule, at any cost.
With this view of history uniting the earth under a single government would require either a single monoculture, or a dictatorial rule forcing a cultural homogenization over generations until the dissenting voices have diminished to insignificance.
Perhaps our beloved internet will function as a vehicle of such homogenization - it's not completely impossible.
Note: There was no large war in europe between the napoleonic wars and the first world war. Historically, europe has been quite pieceful in the past without a huge bureaucracy attempting to to formulate everything under it's legalistic framework.
I believe in western concept of human rights, and I do not believe in cultural relativism - oppression is oppression. But, a world government is a concept that is very problematic in our current state in history. I have no idea if this will change.