I am Jewish. The Jewish Bible and Talmud commands Jews to slaughter animals this way. And yes, if done correctly, the animal should go unconsious pretty quickly, thereby giving it no pain.
But I do wonder if Rabbis do indeed watch EVERY single slaughter, to make sure the animal is immediately unconscious and quickly discards the animal as "unKosher" if it does not.
Meat and poultry is about money, and I would not be surprised if religious obligations are set aside in the name of profit.
But I am still not aware of any Jewish rule that says the animal cannot be stunned before its throat is cut. Perhaps you can enlighten me.