I think that filming the kill takes something away from the sacredness of the event, and the very fact that I have been given a gift to be the unique individual to experience those precise moments. Instead of a great story told at camp, it becomes an analytical procedure of sorts. And there is no imagination required by anyone because a video is the next thing to actually being there.
For teaching purposes, I think they have their place. I used to enjoy watching videos, but I've come to the point where they are all the same, boring, self-promoting exercise. That probably soured me, too.
In addition, I have no desire to blow shot opportunities when messing with camera equipment. I have no problem with pictures of the hunt, camp, game killed, etc. though. In fact, still photos write the story of the hunt and leave our imaginations to take us there.
Another thing that I feel very strongly about is standing over or filming an animal as it dies. I will never do that. I can only imagine what it would be like to have a predator standing over you as you breathe your last (even for a prey animal that lacks the ability to rationally think). If I need to administer a second shot, I do. But then I walk away for a few minutes and let that animal have some peace. Might sound "soft" or weird, but any animal in my book deserves that respect as it dies from a wound that we inflicted upon it. My $.02.