A bat which has less mass, and especially which has a lower moment of inertia, may be swung faster.
Lowering the mass (and moment-of-inertia) may increase the bat swing speed, but the lower mass means that the collision between bat and ball is less effective. If the swing speed is kept constant, a heavier bat will always propel the ball faster and farther. So removing mass from the bat will actually reduce the batted-ball speed.