Translation: I live in California and have no friends, as evidenced by my anime avatar.
When has diversity not worked? The most stable nation-states in the world today are the product of diverse groups coming together and forming a shared identity while still maintaining their uniqueness. Americans tend not to realize this, but so-called "homogenous" countries like Britain, France, and Germany have had very pronounced cultural differences among their comprising regions.
The fact that conservatards think "Balkanization" is a consequence of diversity betrays a basic misunderstanding of what diversity is. Balkan cultures really aren't that diverse from each other. At least, they are no more diverse than a Parisian is from an Alsatian. Yugoslavia broke up because of political seeds that were planted in WW2, not because of diversity. Balkanization is simply the continuous breakup of a large polity into progressively smaller ones.
Do you know any Bosnians? I know a few, and they are quite different from other slavs that I know including other people from yoguslavia. I know quite a few Bosnians that hang out with Turkish people. I don't know much about the Serbian wars other than I watched it on the news when I was a 12, but based on my experience with Bosnians as an adult I can see why they would volley for their independence.
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The Mongols came together under a shared national identity. That is the definition of a nation. It's the broadest form of of commonality. However, I must stress that there is usually something shared. Nations don't seem to form from a arbitrary collection of human beings. Broad commonality is how the stable nation-states of Europe formed. However, you're right that these euro nations have diversity even without non-european immigration. The Sammi, the Basque people and many others are examples. In most cases though, they have not integrated (after more than 100 years) and see themselves as something other than french, Spanish or Norwegian and independence movements exist in these ethnic groups.
Ask yourself this..
If you are a black person, do you look at a white person on the street and say to yourself, "that's an American brother". Some people might, but I seriously doubt most people have that sense of brotherhood when it comes to their interactions with other races or ethnicities in the type of diversity that is enforced in the West. That sense of brotherhood comes almost naturally within a nation.
There are so many "nations" in the united States that a breakup is almost destined to happen sometime the future.
