It makes no difference why he wants to kill them it takes the same amount of energy to kill them either way. A .243 will kill an elk. I have a rancher friend in Idaho who kills a nice elk with a 22-250 every year. He sits in his blind and head shoots them when they come down to feed on his ranch. It is not often that you can create the situation where you have a good rest and a clear close head shot on an elk. It works for him but would not work up the mountain in the trees and brush. One more point, elk almost never attack when wounded or flushed out at close quarters big bear do.
It makes quite a bit of difference if you are seeking out bears in heavy cover, or if you just shoot them when you see them in fairly open pastureland.
My point with the elk example, is just that some people with lots of experience can find that something works very well for them, that may not work so well for everyone else.
People make out big bears to be monsters that absorb huge ammounts of lead and are hardly affected. Most of the problem is placement and well designed projectiles.
Bell’s 7mm elephant gun worked for him because of precise placement, superb marksmanship, and excellent projectiles.
I do not know of a .243 projectile that I would like to use on big bears, but if a big bear needed killing, and I had a .243, I would not hesitate to use what I had. If I had a choice, I would stuff it Barnes 115 grain bullets.