I suppose there are many reasons why Jesus came. He came to die, yes. But also to rise. Can't have one without the other: "And if Christ be not raised, your faith is vain; ye are yet in your sins." (1 Corinthians 15:17) And He came to serve, yes: "For even the Son of man came not to be ministered unto, but to minister, and to give His life a ransom for many." (Mark 10:45) He did and does all of these things for love, and because His Father asks.
"for I do always those things that please Him." (John 8:29)
The second of Aristotle’s "Four Causes", the "Formal Cause" states that there must be something that the thing, the "material"—that substance of which a thing is comprised and formed—is becoming. For something to come in to existence, there must be (for lack of a better term) an invisible space in which the material will take shape and fill and form into. A void waiting to be filled, so to speak. After Jesus came and left, He essentially formed the church. Starting with the twelve apostles, the body of Christ was born and it continues to this day. And our cause? It's the same as what Jesus' expressed to Pontius Pilate. To bear witness to the truth of who He is:
"Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth." (John 18:37) See, we cannot testify to Jesus as anything less than who He said He is. And for the church, Jesus is, quite literally, that formal cause. There's a purpose for us as individuals in our body, and a purpose for the body, as one. Jesus' prayer in John 17 brought about the body-as-one and the Holy Spirit moved at His insistence to make it so.
Taking all of this into account, another reason that Jesus can was to form His body–us. And He lived it out to give us something to be and become.
It's an apt analogy, to be sure, but Paul compares the body of Christ to an actual body. "For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit. For the body is not one member, but many...But now are they many members, yet but one body." (1 Corinthians 12:13, 20)
When Jesus prayed in John 17 (verse 22), "that they may be one, even as we are one", He was essentially "forming" the future body of Christ as one. Wrap your mind around this. Aristotle's "Formal Cause" is the template which a "thing" becomes. And Jesus made that template of oneness when He petitioned His Father to make us one. The blueprints have been drawn up, all we have to do is step in time.