Texan
The grip has a direct effect on how the ball reacts at the release point. That was the thrust of my original point.
The grip can cause drag coefficient characteristics that emulate a similar effect dragging the foot.
In the discussion I have never advocated a "monolithic" approach to these techniques.
As I have taught my son to use the three arm slots, overhand-elbow at the ear, 3/4 arm-slot elbow, at the shoulder, and sidearm-elbow, slightly below the shoulder, when he throws his slurve.
In fact the best pitchers will use a variety of techniques and grips to do several things. For instance, some coaches have eliminated the "slide step" pitch out of the set position. They advocate using solely the "live leg lift". Problem with this approach in my opinion it allows the runner to get to large a jump. IMO a better approach is to alternate both the number of times in checking the runner and use of the slide step, and alternatively the live leg lift. I have taught my son to alternate all three techniques, quick pitch-no look, slide step and live leg lift with random checks so the runner can't time the pitchers body movements. Very seldom does a runner steal a bag when my son is pitching.
Similarly, the grips can provide a variety of speeds without any change whatsoever in the mechanics.
But there is a big difference between the effects of the grip and the effects that the three arm slots have in conjunction with a proper "tempo" in the rhythm at the release point.
In my opinion Juan Marichal of the SF Giants is the consummate pitcher of pitcher's because he used a variety of different pitches he had that he could throw for strikes, he knew how to pitch using changes in speeds of several different varieties. I saw him throw a double-header back-to-back, and one game that went 15 innings. They don't make them like him anymore.