I've heard several things in here that I think people are confused by. It's not about accelerating THROUGH the cueball. It's accelerating to the point of contact. Do you know why letting the weight of the cue do the work works so well? It's because it's impossible to decelerate prior to contact if you're just carrying the cue to the point of contact. If you're not trying to force the cue through the ball, you don't have the means to decelerate without absolutely intending to.
Letting the weight of the cue do the work does more than just that, it makes it harder to deviate off of the intended aimline, to deviate from the intended portion of the cueball you wish to contact, etc.
