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.
I’m not sure what you mean by “suck it and see”. Your post was about cone shape. Good speaker design is full of challenges. But cone shape isn’t one of them. Buy what sounds best to you. 
What I meant by "suck it and see", is reading the posts, despite any science or past design experiments, be that of cone shape, cabinet or any other aspect of the speaker design, the bottom line seems to be you have no guarantee that it will sound any better to you than something put together in your garage out of available parts. You design it, build it, take all the available measurements, but it's not until you listen to it, do you find out how good or bad it is. Just like a new recipe, despite having all the best ingredients you don't know until you taste it. Add to that the fact that tastes in how speakers sound vary, along with all the other variables, and what you said becomes the deciding factor be they $$$ latest tech or not, if they sound good to you, they are good.
to the OP,
Let's go back to understand what physically is happening to the cone. The voice coil attached to a cone will move the cone when the voice coil moves forward and backward. The entire cone does not respond all at once. Instead, a compression wave and a bending wave is launched into the cone by the voice coil. The compression wave causes no sound. The bending wave travels down the cone and induces a compression wave in the air.

As the bending wave travels to the far edge of the cone (at the surround), the air compression wave travels away from the cone surface. Due to the difference of the wave speed in the cone and the wave speed in the air, the effective wavefront at the plane of the cone surround can vary from a concave shape to a convex shape, with a plane wave between the two extremes.

Since the speed of the wave in the cone is typically slower than in the air, the cone angle can be designed to produce a convex spherical wavefront from the cone, propagating out  of the speaker into the forward half-space.

In the specific case of the Walsh speaker design with the apex of the cone pointed upward, the cone radiates sound from the convex side of the diaphragm. Since the sonic velocity in the cone much higher than in the air, a cylindrical wavefront is propagated in a 360-degree horizontal direction. With appropriate control of sound speed variation in the diaphragm, a waveform can be made to be spherical, radiating like a point source over a wideband of frequencies, without crossovers.

The reason most electromagnetic speakers use multiple drivers is that the designer wants each cone to move a if it were a rigid surface, which it's not. So the cone is restricted in frequency range where it acts as if it were moving all at once. For higher frequencies, a smaller driver is used to act as if it were moving all at once, because the wavelength in the cone (and in the air) is much shorter than for lower frequencies. And, so forth, which means you need crossovers to direct the right frequency range to each driver.

Many thanks,

I have a better idea of what's going on, and it gives me more to research.