That's not the only reason. Kosher law (and I think halal, correct me if I'm wrong) says the animal must be treated humanely, and in the days before bolt guns, slitting an animal's throat while upside down was a very humane method. I know people are emotionally moved by watching videos of this stuff, but the animal loses consciousness very quickly, most of the writhing around is pure reflex. Ever seen a chicken after it's been decapitated? The body keeps moving around for a bit-- pure reflex, which is why many farmers prefer to wring a chicken's neck than chop it off.
People are obviously moved by watching videos of this stuff because we live in cities, get our meat prepacked and most of us do not experience this sort of thing. It is not a normal thing for us to see. But that is how you get your meat, whether you like it or not.
Exactly. Modern urban society, especially in more well-to-do communities, has become very divorced from the dirty realities that provide the foundations for their society's very existence, and when shown some of these things, people living in that environment can become very upset (is it any wonder that most animal-rights activists are from the middle or upper class?). Now that's not to say all these dirty little realities are just things we have to live with-- some are plainly abhorrent and should be fought (though I think the fight on many issues has to come from the working-class). However, it also means that certain dirty things that are out of the everyday experience of an urban middle-class person can seem a lot worse than they actually are. This is a good example. Relatively speaking, koshering is a humane way of killing an animal-- not as humane as stunning first (which I would definitely favor), but not nearly inhumane enough to start running roughshod over people's right to the free exercise of their religious rituals. I have a feeling that those who have never killed anything more than a bug will have a different opinion on this subject than those who actually have killed before.
Although I disagree with her on this and other animal welfare issues, I think Cheetah raised a very good point that reforming factory farming needs to be way higher up on the list of priorities. After all, there is no religious component to that, and it is, in my opinion, not just an animal welfare issue, but a public health issue as well.