Most hunters rarely hit their animal perfectly and kill it instantly on the first shot. You need to Follow Up!
While we all should strive for first-shot kills, this is the real world with wind, brush, moving animals and excited/tired hunters. A second shot needs to be instantly available, and an an accurate one if fired.
Preparing for a follow-up shot, even if it isn't needed, is just good gun handling. No matter how you called that shot, you should immediately snick the action and stay on target. If the animal stays down, fine. If not, you're prepared.
This prevents that incredibly annoying habit of "shoot and gawk" where the shooter, after touching off a shot, takes the butt out of their shoulder, leaving the empty case chambered, and looks downrange to figure out what just happened. Watch nearly any hunting show for a demonstration of this novice mistake.
In practice, a hunting firearm should normally be fired in both singles and controlled pairs, with the exception of group shooting and zeroing. By firing pairs, on the clock, the hunter-shooter will eventually master their chosen action. Even when firing singles, you should develop the habit of bolting/levering/pumping before the butt leaves your shoulder and the chamber should be loaded before the empty hits the ground.
This is so important that it is incorporated into the HunterShooter rules, with Procedurals assessed for those that forget.