Sinning animals alive is impractical because they squirm around too much.
Besides usually the pelt or skin is a byproduct of meat production. So you stun the animal to stop it from squirming and then you want to bleed it with the heart still going because leaving the blood inside will spoil the meat.
You also want to have the animal calm because an excited animal will result in a mean condition known as PSE. All that adrenalin and other hormones causes the meat to taste funny.
In a lot of Middle Eastern countries, they hold the animal down and cut its throat without first stunning it. But in the United States, we are humane and knock the animal out, with a bolt to the brain or by electric shock.