Mainly because moving them to an elephant reserve costs a good amount of money (something like $5000 per, if I recall correctly) and it's cheaper to just shoot them. His hunting trip was probably more expensive than that.

My understanding is that elephants are being routinely culled on reserves, as well. They eat. A lot.

(I don't mind the downvote at all but it's be good to know if the downvotes connote the fact that I'm wrong; I may be!)

A cursory googling for "elephants culled on reserves" shows several stories from reliable sources indicating that you're not mistaken.