To the Magi, the loss of their traditions to impending Christianity is like staring both death and defeat in the face at once. Death doesn't make its real entrance until the end of "Journey of the Magi," but when it finally does sashay onto the scene, it puts all too fine a point on what the coming of Jesus means to the Magi and their people.
"Journey of the Magi" makes poignant commentary on the fact that Jesus was literally born to die. That's the real gist of the poem—not the Magis' long-lost way of life.
The spiritual death of the Magus is horrific enough for him to wish for actual bodily death, too. It's extreme, but for him, it's the only solution.