As this novel explores the concept of expiation, Finny's death becomes important. Not only does Gene need to find a way to forgive himself for knocking Finny out of the tree, he has to forgive himself for his role in Finny's death.
The novel begins years after the events as Gene is finally ready to come to terms with his guilt and his regret.
...it is only as a thirty-something adult revisiting his former school that Gene has accumulated the wisdom and maturity to fully understand the significance of what happened in his adolescence.
In telling the story of his last year at Devon, Gene admits his part in Finny's injury, an admission which is not at all easy for him to make, as evidenced by the long interim between the events and Gene's acceptance of his part in them.
Taking this specific maturity and expiation as the central interest of the novel, Finny's death is warranted.
Furthermore, if we read Finny's character as a symbol of youthful innocence and exuberance, it is again fitting that he should die. Gene's innocence, like that of all the boys, is lost in the end. For Gene this happened before going to war, but for all the boys leaving Devon meant leaving innocence behind.
Finny, as the symbol of innocence, could not go to war and could not leave Devon like the other boys.