I recall reading something many years ago on this topic and it really set me back and made me think. The author suggested that Lincoln died at precisely the moment that was going to turn him into a national (or at least a Northern) icon. Had he died a bit earlier, before the fall of Richmond and the surrender of Lee, some other president would have garnered some of the laurels that were placed on Lincoln's head. Getting shot on that Good Friday, 1865, assured him some kind of apotheosis.
But then that person went on to say that if he had lived out his second term, that his reputation would have foundered on the shoals of Reconstruction, that the task was so difficult, so impossible to satisfy an angry North, a sullen South and an expectant African American population, that his presidency would have been forever tainted by this failure and his stature forever diminished. That person concluded that the timing of Lincoln's death was absolutely the best possible time for him to ascend into the Elysian Fields. We probably consider such a thesis with much distaste but I think that author just may have been right.