With a .223 going 3000+ fps at 100 yards and under, the time between when the hammer starts to move and the bullet arrives where it's going to is measured in milliseconds; a deer is not going to move very far in that time. There are also clues that an animal is going to move before it does. If one sees them before deciding to pull the trigger, one should not fire. And one should learn those clues, either through observation of deer in the wild while not hunting, or Dr. Ken Nordberg's excellent series of books on game animal behavior.
If you are talking 500 yards, then the time is such that your scenario of the animal moving enough to cause a wounded animal is more likely. If you are talking a slow round at long distance, say .45-70 at 500 rounds at a buffalo, yes, they can walk away before it hits, without even knowing they've been shot at. Animals moving before it hits is even more likely with bows. Infinitely more so if one's idea of accuracy is pie plate at 100 yards from a bench, or even 50 yards as I has so often seen at 'sight-in' days.
It all amounts to level of hunter education and ethics. When I was 15, I snap shot at a doe that jumped up right in front of me; my Dad's best friend had to track it for me, (taught me a lot about tracking in that situation) and put it down when we found it. I learned a lot about hunting ethically then, and I never forgot it. He was my role model for an ethical hunter. That guy killed a moose with a .30-30; he did not have to track it.
I have had two deer I've shot take off like drag cars after the bullets hit them, and even with their aortas in shreds still went 50 and 75 yards. Both deer were in a high state of alert , one having just been shot at by someone else, the other chased through a swamp by another hunter who thought he could 'sneak up' on it. But they were both staring right at me when I shot. Neither moved a muscle until hit by the bullet/slug. Making noise to stop a moving deer causes them to stop and it gives you about 2 seconds to fire while they try to discern what you are.
True, however, I'm sure FL-NC will attest that well-aimed rounds from an AR-type rifle will put humans down consistently also. I do not have personal experience with that, and I hope I never do. But I do know that there are many bullet weights and designs in .224 diameter that make the AR in .223/5.56 a versatile caliber for game. I choose to use a Varmint type bullet for both varmint and deer (Nosler 55 gr. Ballistic Tip Varmint) because I know that it will kill a deer within the self-imposed parameters I have. Those with looser parameters ("If it's brown, it's down") would be better served with a round that has different terminal ballistics, say .50 BMG.
