I would guess that this is because the longitudinal waves would have to move through the focus of the parabola/circular section, dispersing the wave in all directions in front of the speaker (and behind, depending on the acoustic shielding).
However, if a subwoofer was made from a circular triangular surface section, whose height is the same as the radius of the circular section:
Would this make the subwoofer directional? I.e. could I point at someone very far away and it would be heard but wouldn't be heard by those not in it's path?