I have a feeling that was added for dramatic effect for the movie as I’m sure the actual ritual doesn’t say the priest should kill himself. Having watched part of the movie recently, I think the character of Father Karras, was a bit tormented himself, not by possession though but personal demons so to speak.
As I believe the real case that the movie was based upon, the priests lived at the end. In fact, I saw one of them interviewed recently on a special about demon possession. At the time he was a young man studying for the priesthood and was taken along with the Jesuit priest who did the actual exorcism of the little boy, who apparently remembers nothing.
The priest said he truly believed he was witnessing a demon possession.