In order to control the cue-ball a properly shaped tip must be used.
It allows the cue-ball to be struck far more accurately.
Consider Diagram 1.
The cues on the left have square flattened tips, while the cues on
the right have tips which have been shaped into a dome.
Notice how the lefthand cue moves across the ball, but only contacts the centre; and
how the righthand cue is able to strike the cue-ball at any point within the same range.
These striking positions give experienced players far more control, and are used to
great effect in both the 'stun' and long distance power shots.
The cues at the top of the diagram again illustrate why the flattened tip should not be
used. The domed tip of the righthand cue allows more of the surface area to contact
the ball; but as the lefthand cue moves away from the centre, only the edge of the
tip can make contact, making a miscue far more likely.