It could easily work well, but I think there are possibly some practical concerns. Carbon fiber doesn't play nice with cutting/shaping tools commonly used for working on wood necks (i.e. carving with a rasp could be problematic. And I wouldn't want to shape such a neck with a power carver since it would throw dangerous shards of carbon fibers all over my workshop). I have never tried what you're suggesting on a bass neck, but I have done lots of carbon work in other hobbies over the years, so I'm speculating a bit here based on that indirect experience.
On the other hand, I do think you're on to something in terms of the best application of carbon fiber in a bass neck. Putting bars directly under the fretboard isn't "efficient" in terms of making good design choices on the use of the material. A neck is basically a beam - the back is under tension and the fretboard side is under compression. This is a problem if you're trying to design for stiffness - the back is smaller in profile (less wood), and usually the fretboard is made from a stiffer material (ebony, rosewood). And wood is bad under tension. So, necks tend to be too strong on the fretboard side and too weak on the back. Hence, putting a carbon rod right under the fretboard isn't the best location, you're adding stiffness where it's least needed.
If you search on the subject, you'll see that a handful of the builders on here have arrived at an alternate design. We put raw carbon fiber tow under the truss rod. There are a couple of different popular ways to do this, but the result is the same - carbon fibers down deep in the neck, as close to the back as possible, where they can make a big impact (since carbon is much better than wood under tension). Three or four small strips of tow - less than 1/16" thick - provides plenty of stiffness.
But in all of this, I think it's important to consider the ultimate goal. Are you trying to achieve maximum stiffness? That's a dangerous game in and of itself. It's easy to make a bass neck so stiff that the strings and the truss rod combined can't pull enough relief. So, ultimately, there's no real serious need to "maximize" the design, and it boils down to practicality and process - how does the material fit into your workflow? For me, it's really easy to add tow under the truss rod, so when I think a neck needs more stiffness, that's what I do. The only adjustments to the process are cutting the slot slightly deeper. It's less work and less time (and much less cost) than putting pultruded bars in their own channels on either side of the rod. And it's probably easier - less mess, less potential issues with carving - than putting laminates vertically in the neck. But you may arrive at a different answer based on how you work.
