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.
chris_w_uk
Put a whole bunch of small...say 3"...full range drivers in an array of some sort that will move enough air to get to 85+ dB and be prepared at the amazing sound...with no crossover interference...that all these little drivers working in unison can create. 

Faital Pro makes some pretty killer little full range drivers for about $20 each.
Essentially the old Infinity. They had some good ... and some bad. I am a fan of midranges in this size. Not many really good. 
Well this has been interesting.  So though there is science involved and calculations to make, and I dare say the implementation of aspects of others previous design successes to assist with the design of a good speaker system, the bottom line is once you have done all that and built your speaker, suck it and see seems to be the final process.
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.