In short
Jesus healed the servant without going to him, because his presence in the centurion’s house was unnecessary, and healing while not present showed the power and authority of his words.
Jesus did not proceed to go to the house of the centurion, for it was unnecessary. He simply spoke the word he requested, upon which the servant was immediately healed. This reveals that the words of Jesus have power and authority. He simply speaks and it is so, for it was indeed his words, uttered in response to the faith of the centurion, that effectuated the healing of the servant.1
13 And to the centurion Jesus said, “Go; let it be done for you as you have believed.” And the servant was healed at that very moment.