There is a concept in skill development that the faster a person has to execute a skill, the higher the error level. It’s especially crucial in team sports but it shouldn’t be ignored here. When the whole arm is used to deliver the momentum the less the hand feels like it has to get involved in the production of velocity. The extra mass helps create the same momentum with less velocity. There is a sense of more control when the hand takes a back seat to the arm delivering the cue. The difference is subtle because the elbow still has to hinge in a synchronous manner. Coordination learned through a pendulum stroke definitely helps. For me the chief difference is that there is more arm swing rather than an appendage simply hanging.
Once you expand your experience to include different ways to deliver the cue, if you trust your subconscious to pick how to achieve a desired effect, it will pick what it tells itself will do the job most efficiently. When we first try something new if we succeed we tend to keep doing it that way. That said the minute performance suffers our stress level goes up. The tendency is to revert to the familiar, a comfort zone of sorts, only looking to lower the stress. While pushing the envelope, of our current skill set, is how we learn, the envelope has an elastic quality, wanting to retreat to the old. Interestingly enough though if we stretch it far enough it can never return to its original bounds.
Learning to follow through on shots is more a byproduct of what the body has learned to do. It’s a natural result of what the body has learned about what comes before impact, an effect rather than a cause. It’s a result of how the body senses the shot.