I'm a noob here, but I'll jump in 'cuz I do have some experience with aircraft composites. I think one of the bigger issues would be the fact that you probably couldn't use conventional rivets. The swelling that occurs during installation would damage the composite. Not necessarily a show-stopper, but it would require some re-engineering. All your connections would probably need to be screws and nuts (carefully torqued). Boeing had quite a time designing the wing-to-body attachments on the 787 to give them the strength and fatigue life they needed.