If God had meant us to be united as the ideal way of living, he would not have confounded our language

And Jehovah came down to see the city and the tower, which the children of men builded. And Jehovah said, Behold, they are one people, and they have all one language; and this is what they begin to do: and now nothing will be withholden from them, which they purpose to do. Come, let us go down, and there confound their language, that they may not understand one another's speech. So Jehovah scattered them abroad from thence upon the face of all the earth: and they left off building the city.

-- Genesis 11:5ff.

The ideal of unity in John and Paul is of a different inspiration entirely.