It just occured to me:
DN makes no sense at this point! (well within the fictional boundaries of the manga)
Let's assume there is a "fixed" date, when a person gets killed (like MIA by getting stabbed to death by stalker, or she getting killed by the police because of her "KIRA" doing) and a Shinigami would be killed, for altering the "fixed" date.
Then Shinigami would be killed by default, if they kill anyone, since your life can influence so much (like causing traffic jams and thereby fatalities , soldiers etc) other lifes, that it is impossible to kill someone wihout alterting the "fixed" date of other persons.
But Shinigami need to kill people in order to prolong their lifes!!!
hence the "Eye for 50% from the rest of your life trade" and the "I get the rest ofy our life"