Speaker cone shape

Why are speakers cone shaped, apart from rigidity? To my mind the air being pushed by a cone would radiate at an angle inward toward the axis of the speaker and collide in the centre, which seems inefficient to me, and likely to cause some distortion of the sound. This may also cause interference to adjacent speakers on the same baffle.  Would there be any advantage to having the surface flat, assuming you could maintain rigidity without increasing the mass? There must be modern capable materials out there.
Is the fact that the speaker is cone shaped that causes the volume to change counter intuitively as you move left and right in front of the speakers? What I mean by counter intuitively is when you move left the right speaker sounds louder and visa versa.