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

Carbon Fiber is an expensive material and very time-consuming to do properly. And very difficult to do at scale. If you want to see what's involved in making CF parts, I recommend spending some time on the Easy Composites YouTube channel

How many violins or highly regarded guitars are made out of carbon fiber?  Pianos?  Just wondering.

All things resonate carbon fiber does so and it sounds plastic-like. Wood resonates and if done right can be low in level and even in frequency this sound good and doesn't detract. Alunimun is a cheap material marketed as a luxury item in audio because audiophiles don't remember that it's used in beer cans.

Sorry, johnk, but this is wrong:

Alunimun is a cheap material marketed as a luxury item in audio because audiophiles don't remember that it's used in beer cans.

The machined aluminum cabinets by Magico and Rockport (for example) are both complex and very vexpensive to make. No one applies more engineering to their speakers than those two companies, imo (there are others on par I assume). 

Rockport has combined a carbon fiber exterior shell with an aluminum interior housing for their newest speaker, which saves some money. Their top of the line speaker uses aluminum interior/exterior shells. Magico is all aluminum. 

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

The answer is no. All materials have specific characteristics and need to be used correctly and in the right application. No material is inherently superior across the board, including aluminum or wood.

Actually Rockport used cast aluminum enclosure sections which is very different than machined cabinets. Magico used extruded and machined section. Their designs have more to do with the implementation than the materials. 

We just concluded a year long evaluation of different materials, including cast aluminum and carbon fiber, for our Gen 2 Apollo speakers. For our speakers design we found that a fiber reinforced molded custom engineered polymer had the best characteristics. Cost is between aluminum and composite, aluminum being the cheapest.