As I understand it, it really isn’t that so much as the odd rogue bull who won’t play nice with people or other elephants.
Elephants are highly social critters and the elderly are normally their leaders. Killing them just because they are old would definitely adversely affect the herds.
However often in herds the eldest or alpha male gets to mate with all the females (unsure of elephants but in a lion pride this is the norm) If this male is not fertile the pack will die out unless a stronger younger male challenges for leadership.