I know folks that swear by the center fire .22s and are careful shots. It’s a more than adequate gun for them BUT they’re typically in the open and either are a good enough shot the deer are DRT or they can see the deer fall after a run. Where I hunt, I really like an entrance wound and an exit with a good blood trail. Lots of palmettos and I’ve trailed many deer where there was never a drop of blood on the ground, it was all on the palmetto leaves. A centerfire.22 won’t reliably give an exit, so I won’t use one but they’ll certainly kill a deer, I just don’t like to spend that much time looking for them.
