The simple answer is that the only way to make the deer 'not move' is to paralyze it, and you do that by hitting the brain or spine. The reason people who shoot neck shoot there is to sever the spine. Also, if you shoot high on the animal, the shock to the spine will paralyze the animal. The other alternative, hitting the shoulder of the animal, causes a) shock to the spine by trauma to the shoulder, b) a broken shoulder, and c) increased overall trauma by i) increased mushrooming of the bullet, ii) or splintering of the bullet, and iii) bone shards.

Drawbacks:
Brain - that's a pretty small target, and the deer's head is in almost constant motion. I would never suggest anyone shoot for the brain, unless it was a follow-up shot.
Neck - again, small target. If you miss the spine, you hope for the artery, and death by immediate blood loss. If you hit the trachea or all that other neck where there's nothing vital, the deer's not gonna die very quickly at all, and you might not have a blood trail to follow. Miss where you're aiming on one neck shot and you might never neck shoot again.
Spine - it's right there on the back. Shoot over by an inch, and you've got a living deer.
Shoulder - destroyed meat. The overall meat loss isn't actually that much, though, if you do a good job butchering. Unless, of course, you're shooting a magnum or something.

I always, always shoot for the classic heart/lung area, although I do tend to hold close to the front shoulder and clip it sometimes. Every shoulder shot I've ever taken has fallen where it's stood, and I never doubted the shot for a second, unlike how I'd feel if I took a neck shot.