All the hospitals in my area will not allow video taping of births. The will not allow pictures of the actual birth either. I didn't want a video, would have liked pics but wound up having an unschedualed c-section.
I videotaped my DD's birth (4) years ago. I watched it once after she was born, and now have no idea what I did with that tape.
I am now pregnant with my 2nd, and have no interest in taping this one.
I have enjoyed the pictures more than the video we made. Neither were in my bubble, but had a nice side view of the birth. I wanted my kids to have memories, not nightmares. I think that either is fine, as long as it is done in good taste