I believe that the throat cutting method isn't any LESS humane.

If I remember correctly (and I may not), the biggest reason why the slaughter houses don't use it is because it's inefficient. They do drain the blood (and collect it to sell), but they do it in motion by running the carcasses along the line over a trough (essentially).

If they had to actually kill the animal that way, their production times would slow down, because you couldn't dress the animal or move it on down the line until it was dead.