If you've missed the first, you may well miss the second too
Not only that, but the quick second shot is a bit mythical really. Whether your quarry is hit, wounded and flapping about like a flappy thing, or its dropped in a place where you can't see/hit it, you never get a clean second shot, no matter how fast you reload.
Never seen a rabbit take a bad hit and sit there waiting for me to finish it off.. Never seen a pigeon not either fly off instantly to drop a hundred years away or drop flapping from the tree into cover.
Real life, and in theory.... very different beasts.
Quick second shots are good if you miss the target completely and it doesn't move, giving you chance for another. But if thats happening, you should be shooting targets some more.
There is no such thing as a 100% one shot - one quick kill situation.
Even of you are a very accurate shot, the gun spreads which can mean just a wounding hit.
Most of our history we hunted with projectile weapons with a slow second shot, but then we did not worry so much about the humane quick dispatch.