The ending of the story is an instance of irony. Suppose Paul had not died at the end, how would you have reacted to the story?
It is true that a tragedy digs a deeper mark than a happy ending. It causes an emotional catharsis in the audience. Had the story had a happy ending it would have been pleasant, however, the reader would not have felt the emotions and passion that drove Paul to his inevitable climax. Yet some may find it not justified to have killed the boy at the end of the story that went so well with Paul achieving what he wanted all the while, money and love both. He sacrificed his life to bring to his mother what his father couldn't and thus proved to be worthy of her affection, which hungered for. However, one can not have all the happiness in the world. They say that God is cruel when he gives us something, he gives it to us only with one had while taking away with the other our most cherished possession. So, it can not be said that the death of Paul was justified or other way round; however, it is ironical. Had he lived post the Derby win, who knows what shape the story might have taken. Maybe what happens happens for some good yet it would have brought the story to a happy ending had Paul lived.