The tower of Babel incident shows us that men have a profound desire for the kingdom of God implanted in their nature. The kingdom is an inescapable concept because it is part of what it means that man is created to be like God. God is one and three. Man, therefore, as God's image seeks both to express God's diversity and His unity. For man the sinner both of these motives become perverted.
Unity degenerates into totalitarianism, diversity into anarchy.
It is certain, however, that Nimrod would not have succeeded even without God's judgment. Consider the history of man until the tower was built. As soon as Adam sinned, his relationship with Eve was corrupted. It was no longer possible to keep men from violence. God would have been forced to judge the world again.