As with the story of Cain and Abel, the Tower of Babel narrative has, for modern scholars, certain clearly etiological elements: not only its explanation for the name Babel, but also its accounting for the dispersion of peoples across the Near East and the replacement of an originally single, common language by an array of different, mutually incomprehensible idioms. Behind this latter element, too, modern scholars see a message not about the world as a whole, but something rather more local and specific. Semitic languages all appeared to be related: any native speaker could tell that Babylonian and Assyrian and Aramaic and Hebrew all had common roots and expressions, but a speaker of one tongue would not necessarily understand much of what was being said in the others. It is this reality, rather than the existence of different languages per se, that the story seems out to explain: all the peoples of the ancient Near East did, it says, originally speak the same language, but that unity was destroyed quite intentionally by God.
Of course, once Sumerian had fallen into desuetude, all languages spoken in the area would have been clearly related, and the story makes much more sense.