It has always been my understanding that the method is designed to do exactly the opposite. Small cut to sever the jugular allows for the animal to bleed out. Stunning the beast with a sledge hammer to the head doesn't seem more "humane" to me. Besides, at least in the case of Kosher slaughter (and Halal is more or less parallel) they are rules provided by a higher authority than any government.
I’m for whatever is the most humane and least cruel. I take it that kosher and halal were so a couple thousand years ago. If there’s a better approach now I can’t believe that that would not be the more Godly approach.
But I know there are competing claims and I’m not certain which is correct.