I've been thinking, fundamental things like this sometimes really make us diyers very frustrated.
Cones do matter of course! A lot I think. The interactions among air, cone (materials and shape... etc.), and frame, magnet structure.... etc. are too complex to be simulated. Even the 'pro' can only do simulations to some fractions of the whole thing and try putting them together.
Being a humble consumer, trial and error (including by others) seems to be the only way.
I've heard a driver (paper cone) maniac bought 2 tons of paper pulp just for researching the cone compositions... That was long ago and I haven't heard about his paper cone story anymore since then.
After building several (lousy) boxed speakers, I decided not to try it anymore. I'm not a good enough woodworker to experiment on all kinds of boxes to tell which is better than others. And, even it comes with as many limitations as other types, open baffle eliminates some of the major issues of boxed speakers -- including the cone related ones. So it's the route I take and no return.
Oh, sorry for the OT.