Theoretically carbon could be used to make a DH rim. However, the technology is fairly immature. I'm sure we will start seeing them more and more but currently they're gonna be very expensive and offer very little over an ali rim.
Carbon composites can suffer from internal defects that cannot be seen from the outside, i.e. you can see a cracked ali rim, a carbon rim could be damaged but without NDT there'd be no way of telling.
Stitched laminates and new resins may help reduce these effects, but until then a DH wheel is just takes too much abuse to be carbon composite.
No doubt i'll be proved very wrong soon. I come from an aerospace background where safety is key, you can get away with a bit more on a bike.
This man speaks the truth, biggest problem is the insiduous type of cracks you get in it. There are some technologies on the horizon for (kind of) sorting this out but they just arent ready (or cheap enough) yet. Still, I would hazard to guess that as the technology gets cheaper we will start to see more composite parts in DH.