The doctrine is common, but how people express that doctrine is not. The TLM is the result of the culture of Western Europe, highly influenced by the Roman Empire centered in Rome, and later Milan (and perhaps a few other cities in Italy. Things got crazy late in the Empire). The Orthodox Church is influenced by the culture of Russia, Greece, and the Middle East, depending on which branch of the Orthodox Church you consider. However, nearly all branches of the Orthodox Church use some form of the Divine Liturgy of St. John Chrysostom, or the longer one of St. Basil the Great. The doctrine is the same. It is very similar to the TLM as well, though not perfectly identical. But the Church has adapted, so that each culture may more easily understand the doctrine.
I don’t think that the TLM with Gregorian chant/polyphony should become dominant throughout the world. It should, however, become dominant in the West, because that is where it fits with the culture. In Africa, they should have the same form of liturgy, but the songs they sing should be more from their culture. And I don’t mean current pop culture, no, not at all. I mean the culture of the people as it has been for hundreds of years, fulfilled in Christianity. As the Messiah fulfilled the prophecies of the Jews, and St. Paul showed the Greeks that Christ was the fulfillment of their philosophies, making them more complete and wholesome, making them truly awesome, so too should we present Christianity to the world as the fulfillment of each culture, not the replacement of it. Assimilation and the Traditionalist Movement should move together, and not against each other. Other cultures should be traditionally assimilated.