The basic answer (which applies to carbon fiber stringed instruments too) is that our current understanding of materials science is insufficient to produce a material which exhibits as "flat", i.e. uniform frequency resonance curve as wood. Keep in mind that it takes a lot of skill to select proper wood -- there's a reason reed instruments are made primarily of grenadilla and not any old tree from your backyard :-) .
Consider, OTOH, the fact that I've never even seen a wood mouthpiece. There are many different styles and types of rubber/plastic ones, and some clarinetists swear by the crystal models (and saxophonists looking for giant sound use Otto Link metal mouthpieces). Just pointing out that sometimes there are tradeoffs made in the interest of reliability as well as sound quality.
BTW, I used to play a metal clarinet in marching bands. It sounded crappy but I suspect a properly designed and built model would sound fine, albeit more saxophonish.
For that matter, solid metal 'brass' instruments tend to sound better than their fiberglass brethren. It's just a lot less painful to march with a lightweight Sousaphone, and the delta sound quality doesn't matter a whole lot in a football stadium.