It is true that a shot which only hits the esophagus would be a horrible occurance. Similar the a bungled head shot, where the lower jaw is blown off. However, unlike a jaw shot, I would find it hard to conceive of a bullet hitting the esophagus
alone, and not severely damaging or rupturing the surrounding vital structures (trachea, spine, carotid artery, jugular vein). You mentioned that a strike from a high-velocity rifle cartridge would cause massive blood clotting. If so, this would cause a stroke by clotting the aformentioned major blood vessels. So a neck shot has the advantages of a body shot (high target concentration), without the risk of a gut shot or an escaped dying animal, though in a smaller area.
The risk of an animal moving in the time it takes to make a shot is faced by all hunters, no matter where they are aiming. For instance, on my last deer, I aimed for the heart/lungs. The deer took a step just as I was pulling the trigger, and ( I was very excited, and in that "slow motion" state) I saw the motion right at the same time that I realized that it was too late to stop the firing sequence. Had I not done an split-second over-adjustment, I would have gut-shot the deer. As it was it was a perfect neck hit. But as you said, an elk can move out of the crosshairs very fast, and I believe you. This is a risk no matter where you aim, and a neck shot has the lowest risk of hitting a bad spot, such as the jaw, stomach, bladder, etc in the event of such a move.
This is not to denigrate the heart/lungs shot. It has taken thousands of deer cleanly and humanely for centuries in the past, and will for centuries in the future. But it is not the only clean and humane option.