If the wood doesn't matter then why do dead spots exist (and why do they vary in intensity and location)?
Neck and body wood matter. Fingerboard wood is is negligible.
Think of it like this.....if you have a hard maple wood neck and smear a layer of velveeta cheese on it, the velveeta will have no influence on the resonant frequency of the neck. Ok now go to parmesan cheese....same story.
Now upgrade to balsa wood....same story. Until the fingerboard stiffness >>at the material thickness applied to the neck<< is stronger/stiffer than the thick, hard neck itself, its influence on resonance is negligible.
If your were applying an 1/8 of an inch of steel for the fingerboard and attaching it with a hard epoxy or bolting it to the neck, OK then it would significantly influence the resonant frequency of the bass.
Given that we're talking a fretted bass, the only way for fingerboard wood to have an influence on tone is through the resonant frequency of the neck.
Physics, mechanics, engineering....
You want to spend money on a pretty looking fingerboard, go for it. No problem... But you can't use sound as a credible reason to spend the money.
Dead spots can result from a lot of reasons, including non-uniform strength in the primary neck material, poor witness points at the saddle or nut, bad intonation or defective strings. That is more of a system issue.
I'm not trying to offend anyone here....just trying to bring some science into the discussion.