There are three main sociological perspectives. These are functionalism, the conflict perspective, and interactionism. With regard to cultural diversity in the world as a whole, the first two are in favor of it while the third is less inclined to take sides on the need for cultural diversity.
In functionalism, every aspect of a culture or society has an important role to play. These aspects are like organs in our body. Each organ (and each aspect of society) is needed to keep the whole organism alive and healthy. When we are talking about the whole world as a society, functionalists would say that cultural diversity is important because each culture arose for a reason and is needed to maintain the system as a whole.
In conflict theory, things come about through conflict between groups. Conflict theorists would say that the loss of cultural diversity comes about through more powerful societies like the US dominating other societies. US culture comes to overpower other cultures and destroy them. Conflict theorists do not like this because they tend to want the underdog to prevail.
Interactionism is more vague on this subject. In this perspective, things only have whatever meanings people assign to them. Cultural diversity is not good or bad per se. Instead, it is important or unimportant depending on the attitudes of various people in the world.