If you are referring to nation-states, strictly speaking the title of this thread has a point. The nation-state concept was founded on the idea that each nation, that is a people which was culturally and ethnically homogeneous, should have its own polity, i.e. state.
The nation-state idea has been around for about 200 years, and I believe Greece, in 1830 was the first actual example of one.
If one subscribes to the idea that the world should be organized along these lines, then yes, states should be racially and culturally homogeneous. However, the last 200 years have provided ample examples of how nation-states are far from ideal.
First, not all states were founded as nation-states. The best example is the U.S., which most definitely was not racially and culturally homogeneous in 1776, that is, the people living in the 13 colonies, and those that subsequently emigrated to the U.S. were not a "nation". Mind you, 200 years later, you might consider the residents of the U.S., colloquially known as Americans, as a nation.
Second, nation-states, as the 19th and 20th century have shown, seem to get into a lot of wars. Nations have had conflicting territorial claims, and this has led to a lot of conflict. Consider all of the Balkan wars, both world wars, many of the conflicts in Africa and Asia. The South American wars almost all consist of competing nation-states (although perhaps the South American states should not be considered nations). It is hard to argue that nation-states would be peaceful, especially as it is very difficult to draw state boundaries such that each polity contains just a single nation.
Third, the founded polities, i.e., the states, are rarely inhabited solely by one nation (peoples). What do you do with these other peoples, especially when they are indigenous (or at least have been residing there for generations)?
- You can follow the U.S. example with the North American Indians and basically ethnically cleanse them from the land and then isolate them on reservations.
- You can follow the example of many European nations where minorities are homogenized and forced to join the majority (the U.S. does this too with its melting pot idea for immigrants). As an example, when Greece became a country and expanded to its present borders, there were large populations of non-Greeks (Albanians, Romanians, Slavs). These non-Greeks were Hellenized and now several generations later their descendants are Greek. Mind you, some non-Greeks resisted, and those that resisted were ethnically cleansed. Basically the non-Greeks were given a choice of losing their homes or their heritage, most chose to keep their homes. The behavior by the Greeks was fairly standard across nation-states in the 19th and 20th centuries.
- You can follow some kind of partition system, where the multiple peoples are segregated. Perhaps apartheid South Africa is a good example? Maybe present day Israel and Occupied Territories is a good example?
- Or you can try to move past the nation-state formulation to an idea of a multinational country. Canada might be an example of this, being founded as a state with 2 nations (British English and French Quebecers). But over the last 30 years there has been a move in Canada to accept multiculturalism and diversity and move away from the two solitudes if its founding.
So yeah, one could easily argue that nation-states should be racially and culturally homogeneous. However, it is pretty obvious that nation-states are a pretty poor way to organize the world.