African elephants are over populated in some areas and relocation is expensive, dangerous and often not successful.
Adult elephants have no non-human predators. Elephants like humans have adult teeth that don't regenerate or grow back. So when an old elephant gets health problems or its teeth wear down, it will enjoy a slow death until it is too weak to fight off the circling scavengers. A fifty cal to the brain is a much more humane death, and these "paid hunts" are just that - the elephant is already picked for euthenasia, the wealthy just pay to be the ones to pull the trigger. It funds the conservation efforts.
Also many of the hunts are when its time for an elephant to get a check up, so you go hunting elephants with a tranq gun.