AIR Cagiva used a carbon frame on the 593, yamaha messed with it as well. The big problem was that the frame was too stiff and didn't give the rider enough time to react. carbon technology has come a long way since then and by using different lays and fabric you can "tune" it, its common in road pedal bikes which used to be harsh but are now more compliant than steel or titanium.
Controlling chassis flex is the key to getting the bike to handle, the ohlins gp forks have flexible triple clamps, i can't see why Ducati can't get the chassis to work now, it should even be possible to run different lays for different circuits depending upon the trach and type of corner loads.