Haven't hunted bears, but have hunted a lot of animals in Africa and a monolithic from a .375 Ruger that hits in anywhere in the vital zone puts the animal down right there or within 10 yards; a hit outside the vital zone -- even far outside the vital zone -- slows them down quite a bit and allows a follow-up shot to finish the job. A suboptimal hit from smaller calibers always puts the animals to flight -- always. If you're lucky, you may find them later and get another shot, but very often you won't, even with the services of a skilled tracker.But they don't require multiple shots. I've never had to do a follow up on a moose or a sheep or a bou except with monos. Mono's are slow killers IME. And not 22 mono's. 7s, 30s, 33s. Heavy for caliber lead bullets that are above their minimum velocity upon impact, placed anywhere in the vitals kill no matter the caliber, no matter the animal.
This is because animals don't wear body armor. All north American animals are rather thin skinned. Preditors even more so. Thinner bones to.
If you've looked at moose vs bear bones and hide density and thickness you know the bear has less of both. This is the case for all prey vs predator animals.
The only animals I shoot more than once are bears that need to die where they stand, but that'd be the case for any cartridge.
A 375 ruger into the lungs of a brown bear doesn't kill it any more quickly than a 223 in the same location. Or if if does its irrelevant because in both instances you're tracking that bear. It's not a DRT.
So why not shoot it with the rifle and caliber you can more likely get the cns hit and stay in the scope and on target for the immediate follow ups going for that cns hit?