First, my congratulations to Dr. Dave and JoeyA for their team's super bowl win. There must have been major red beans and rice thrown at the tv and all over the house. Yummy.
I have not read everything written in this thread as there has been too much to read, but I have read much of it. I thought I would bring up one point that may not have been discussed, but maybe one that I missed.
My name is Dave and I am an elbow dropper! And, for much of my pool & billiard playing life I have had a slip-stroke, which I have minimized the last 8 years.
I would like to talk about "feel", not just power gained by the elbow drop. There are a lot of times you need to drag the cueball to create a stop/stun shot from medium to long distance (or a similar touch kind of stroke). I find that an exaggerated follow through helps with the timing of how you must hit the cueball to create the touch necessary to shoot a delicate shot that controls the object ball speed and the cueball. To do this I must drop my elbow.
Although I know, and have been told by Dr. Dave & Bob Jewett that the tip only hits the cueball for a split second so all the rest might not matter, it does to me. For me to generate the speed necessary to execute those type of touch shots and to make sure I accelerate through the cueball for maximum accuracy and control, I have found a long follow through works best for me. I think this could be done keeping the elbow in one place, but I think that would be harder to do with more chance of slapping the ball.
With dropping my elbow after passing through the cueball I am able to be very accurate as to where I hit the cueball. The one area that causes a problem for me is when I need to hit the cueball hard (like a hard draw), I have a tendency to raise the tip up slightly before I strike the cueball resulting in less draw than intended. If I am very conscious and deliberate about it I can over come it, but if left to my natural tendencies, I do not hit the cueball where I intended when hitting very hard - I guess I lift up/drop elbow too soon - but I do hit it hard

. This is not an issue for soft and medium strokes.
Why I even mentioned the slip-stroke is because it is typically a very fluid type stroke, not a mechanical one. This is more in line with the exaggerated smooth stroke which ends in an elbow drop.
My feeling on teaching elbow drop or piston/pendulum stroke is that who cares. I think all beginners should learn to keep the elbow still and stroke through the same distance as their back stroke. It makes sense and it's easy to understand for different speeds. But if someone has a natural tendency to follow-through to the point where there elbow drops, that should not be discouraged. It may show that they know how to accelerate through the ball as you should.
Anyway, I don't know if this added anything to the discussion or its just more hot air, but I thought I'd try.
Another Dave in the mix.