Christianity is no more likely to become unified than "sports fans" are likely to be unified. To illustrate . . . . a die hard Yankee fan and a die hard Red Sox fan, are both, to an outside observer, "sports fans" but they are never going to be unified in the sense that you are requesting.
There was at one time a unification of the church in the manor in which I think you are hoping for. It was the Catholic Church of the Middle Ages, also known as the Dark Ages. It was also in the Caliphate of the Ottoman Empire. It was, on a smaller scale, in the high preists of the Inca's whose human sacrifices caused the streets to flow with blood.
Since the age of the enlightenment, however, theocracy has been absent in western civilization, largely. This is a result of freethinking, applying reason and science, and the result of the masses being able to read. Uniting all Christians under one church is going to be a pretty tall order in this day and age.
Are you willing to forego your particular brand of Christianity in favor of Catholocism? Or LDS? Or Snake Handling, or what-have-you? If you were to unite all Christians, what would be your core doctrine? Which version of the Bible would you use? Would your God be a vengeful, jealous, Old Testament style of God? Or a loving, all inclusive, Jesus-style God?
It is these and literally thousands of other questions like these that makes overall Christian unity an impossibility. When you hold the keys to the gates of heaven, you have power over others. Unless there is some disagreement with the established view of those holding the keys, then there is not going to be any room for future key-holders to pop up. And make no mistake, there is strong gain to be had, by holding the keys to heaven.
B.
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