BrianK74 said:
Precisely. This drives me nuts, and it's not the first time I've heard speak of this old wives tale.
I was taught that the only two pivot points should be ones elbow and ones grip. One should keep a firm but relaxed grip on the butt of their cue using only their thumb, middle & index fingers. The cue should not be against ones palm, if it is, the follow through, (and the shot), will be compromised.
The wrist should stay straight in line with the forearm. The upper arm should be as horizontal as is humanly possible, (read: parallel with the cue). The shoulder should never drop at any time, this causes a scooping effect. The forearm is the pendulum and the grip provides the relief that is required during the forward action of the stroke.
When another pivot point is added to the mix, (namely the wrist), it activates unnecessary muscle groups therefore adding inconsistency. Inconsistency means missing more often and potental and frequent miscues, (though most people will blame it on forgetting to chalk up).
There is only one stroke for any and all billiard games. The mechanics never change, only the speed of stroke and where one contacts the cue ball. The stroke for a draw shot is exactly the same as the stroke for follow & kill shots. One must stroke through the cue ball in all shots to apply the proper spin. Follow through is the key to good draw, not a wrist snap.
Less experienced players think they must stop the cue at the point of contact or pull it backwards for draw. The wrist snap is a similar placebo effect. They are possibly allowing themselves to let the cue go and provide more follow-through motion when they believe "snapping their wrist" is responsible.
Spend some time working on the follow-through and forget about the wrist snap. The fundamentals of great pool playing start & stop with great stroke mechanics.
The wrist-snap is an advanced technique and isn't recommended for all levels of poolplayers. Everyone should start off getting grounded in the basic fundamental stroke that you suggested.
For more advanced players, there is definitely a time and a place for many different stroke techniques. There are definitely times when that technique can be a lifesaver.
Most every stroke can be accomplished by various means. Sometimes some strokes can be achieved more easily and more consistently by certain means.
In other words, every shot is about delivering the cue stick to whitey at a certain contact point with a certain speed through the shot. It's all simple physics. Thus, if you are going for draw, and you hit below center using your arm at speed of X then you will get draw (as long as X speed is able to overcome the friction caused by the felt and the weight of the ball).
You could also deliver the cue at a speed of X, by using your arm for a speed of X-Y, but use your wrist to generate a speed of Y. Thus (X-Y) + Y would still equal X.
Now, there could be a slight difference, because with your arm, X was generated over the length of the stroke (from backstroke to contact to instant of no contact with tip). Thus speed from contact to instant of no contact with tip would be relatively consistent.
Whereas, if you generate the speed of Y with your wrist. Then that increase in speed is generated over a much shorter distance.
So now, if you're trying to accelerate through whitey, then your arm would generate acceleration over the length of the arm stroke. Whereby your wrist would generate acceleration over a shorter distance. By Physics, this more instanteous acceleration would deliver a higher degree of spin.
Now, on the other hand, you could just move your arm at speed of X+Z and generate the speed necessary for more draw (whereby X+Z would be greater than X+Y). More simply stated, Z would be greater than Y. Thus you could generate the same draw speed by using more arm speed than would be required by using arm and wrist speed together.
Now, the question would be which could you do with more consistency:
Generate extra speed by using a faster speed with your arm or
Generate extra speed by using your wrist.
For most, it'd be to simply use your arm.
For those who have developed this ability with their wrist, then this'd be simpler.
NOTE: To put it more simply, trick shot artists have developed very excellent wrist-snap, because they deal much more with the extremes of the game of pool, especially with regards to spin.
I saw Tom "Dr. Cue" Rossman in a demonstration where he hit the cue ball into an object ball in such a manner that the cue ball stopped cold in its tracks, but remained spinning ferociously for at least 15-30 seconds.
As a test: try to achieve that without using wrist snap.
Remember, no movement at all from the cue ball forwards, backwards, left or right.
OK, for those of you who get super-technical, no more than 1/4 inch of movement.
Hmmmmmm..... didn't mean for it to sound like a doctoral thesis....
Your right thought it is a great tension release!!! 
