Are carbon fiber speaker cabinets inherently better than wood or metal ones

Well I would say yes. Carbon fiber cabinets have a huge advantage over other materials...Sound/energy coming off the back of the drivers should be directed away from the thinnest part of the speaker which is the cone. Carbon fibers when done properly are alined to direct the energy away from the drivers. Energy travels thru them at an astonishingly high rate of speed, from memory it is about 18 thousand feet per second. Wood is about 500 feet per second. 

Carbon fiber resonants at a very high frequency, as we know high frequencies are easy to dampen...ping a fine wine glass and then simply put your finger on the rim to stop the vibration. Heavy cabinets vibrate a lower frequencies and thus are much more difficult to dampen as well as taking more time to dampen, thus the hangover or lag, 

Wilson Benesch has done so much research and development. Check out their site for more info. 

patrickdowns -$2700 a ton for billet, baltic birch ply is about $160 a sheet. If you do the math birch ply is more costly. 

Carbon fiber is a great material for many applications because it is both light and strong. That said, no material has been more overhyped in recent times, and used to make all kinds of junk, from cup holders to toilet seats. But do they use it to make acoustic guitars or violins or a bass viola? That would make me skeptical that it's a superior material for speaker enclosures. I'm sure it's a great sales gimmick that adds lots to the cost of a product that is likely to be priced extra high as a result. But better for speakers? Naw, it's just another material, and like others have said, you have to account for its strengths and weaknesses just as with any other material. I think it is way over-hyped but I'll tell you one thing that I just bought that really benefits from carbon fiber- a photography tripod-- where its strength and light weight really makes a difference. I don't find it all that attractive usually, so it would not be my first choice for a speaker enclosure unless it was painted or coated with something. 

Cabinets as a major contributor to sound can be a rabbit hole depending on the manufacrurers approach.  ATC mids and tweeters do not even use the cabinet interior- cabinets are just a "baffle holder".  Use of variable density MDF can make such cabients nearly inert- especially at low frequency where the woofer is working.  (in ATC"s case, the LF crossover is at 380Hz) .   

Yes, there are carbon fiber acoustic guitars available at various price points. They are much less affected by changes in temperature and humidity than wooden guitars. RainSong is one popular brand while McPherson cater to fatter wallets.