It certainly has tonal characteristics and seems mostly noted for a higher end tone that some might call sterile, but then again, the same is often said about active electronics, which can be standard equipment on most custom basses.
A major factor is obviously cost, but carbon can't quite be shaped or changed like conventional wood necks. Typically you'll get only a few choices overall because the necks are made from a custom and expensive mold. Bee, for example, only offered graphite as a 5 string or 7 string neck. Choosing neck profiles, scale length, and string spacing simply isn't as easy.
I think graphite reinforcement has come a long way to the point that even Fender does it. Naturally, nothing will be as stiff as pure graphite necks, but I think graphite reinforcement has offered a very beneficial best-of-both worlds in terms of function, building, and tone.