12-15" Full-range Drivers Made of Rigid Material, Like Carbon-Fiber?

There's a reason for that. A rigid diaphragm of that size will have break-up modes that produce more SPL than the desired response. Some commercially available drivers with rigid cones have break-up mode resonances >20dB louder than the passband response, making them very difficult to use.
 
One of my brief visits (time, job applications, court-case [taking somebody to for not paying me], increasing ennui etc.)

There aren't any current production 12in - 15in wideband drivers using rigid cone materials that I know about. As size increases some form of progressive decoupling of the cone is necessary, and that is usually more practical with materials that are inherently better damped and / or can be molded / pressed into complex forms, varying thicknesses etc. Reinforced paper variations or some form of polymer are therefore generally the preferred option. It's not impossible with rigid or semi-rigid materials -alloys, carbon, kevlar etc., especially with some of the more complex decoupling methods, but cost is likely to be high if reasonable performance is to be obtained.