I helped to butcher a deer that my dad took when we were broke down and snowed in in the Siskiyou Mountains. Spent almost a month up there before we could hike out.
Dad used an AR-7. Tried for a neck shot on a doe. Bullet glanced off of the bottom of the jaw, then off of the base of the skull, travelled diagonally down the neck, hit a shoulder bone, punched through both lungs and the heart, and wound up in the intestines. The doe took two steps and dropped.
Admittedly, that shot could have failed badly. That bullet might have ricocheted in any direction. A heavier caliber, though, would have merely shattered the jaw and passed on. The deer would have died a miserable death and we might have, as well.
My take: the .22 is relatively unlikely to kill quickly, its penetration is unpredictable, but it beats going unarmed.