The swing process is only to the 'plane' of contact.
Once the bat enters that 'plane', the control phase of the swing is over. Just holding the bat during hip turn will produce additional bat speed in the bat's circular path.
Swing the bat to just in front of your body and add hip turn. You will feel the bat speeding up in your hands. This is what is described by the term 'turning on a pitch'.
With the popular swing styles used today, batters who exercise good hip turn will hit the ball foul for a good distance.