One of the biggest issues with this is that it would make overpopulation worse. This planet simply cannot afford to hold an exponentially increasing population without people dying from old age to make up for it
And if you say hat this bespeaks of immortality rather than curing aging, they would not come separately. Aging is the body wearing down, which is what kills most people in the end.
Basically anyone that dies of natural causes would, in this situation, be immortal, barring disease, cancer, murder, etc