Just so you know, I'm a pro instrument neck builder. That's literally what I do for a living, and have been doing for over 20 years. I also build my own line of basses, but about half of my business is supplying truss rods and custom neck structures to other Luthiers. I've built around 1000 custom necks over the years, and I'm constantly experimenting with the structures and reinforcements in instrument necks.
I don't like carbon fiber reinforcing bars, and I don't use them in my necks. I'm not saying that they are awful and horrible, but to me they are just a poor way to do the job. You are routing out a large slot of wood and gluing in a block of plastic. The bars that they sell aren't solid graphite or carbon fiber, they are cast or pultruded polyester resin with some percentage of carbon fiber stranding inside. It's a reinforced plastic bar, which you are then trying to glue to a piece of wood. Unnecessary weight, problems with differential expansion, and the carbon fibers end up in the wrong place, structurally. And I don't like what they do to the sound. Which will probably start the beer bottles flying around here.....
I like carbon fiber, but I buy it in the raw strand form, a thin thread that is called TOW. Where I want to do reinforcements, I rout a small slot, and lay in some West Systems epoxy, and a bundle of the TOW strands. Much better bonding to the wood, higher strength, less total plastic added, and I can put the reinforcement right where it's needed.
For example, to resist the classic 12th fret stretch/kink problem on bolt-on necks, I add a "back strap". It's a small bundle of TOW strands that's set in under the truss rod, running from the back of the heel up to about the 5th fret. It's down deep in the neck, about 1/8" from the back surface. That's where the tensile strength is needed. In cross-section, the installed "back strap" is about 1/16" thick x 1/4" wide, but the result is far stronger than putting a pair of bars up under the fingerboard.
The carbon fiber bars are popular because they are really easy to install, either in factory production, or by hobby builders. That's their big advantage. Manufacturers like them because, like Joeyl points out, it allows them to be less fussy in selecting boards for their necks. Slap in the plastic bars and fewer necks come back on warranty. And they are a great marketing hook. Carbon Fiber Stiffening Bars for Increased Stability! I mean, everyone wants Increased Stability, right?
But they aren't needed in well-built necks. They aren't needed for strength, and a well-built neck won't have stability problems. There are many ways to make necks stable without gluing in plastic bars.
