Its completely possible to do a study like this. We have incredible technology for measuring things these days, and the philosophy of science, statistics, and our models for the physical world are advanced enough to figure this out. Basses aren't in high energy environments, working at quantum scale, or near black holes. We can model and measure what happens. There is an answer.
I think the main problem is there isn't so much INTEREST in doing so. What practical purpose is there for figuring out whether tone woods affect tone on electric instruments? Only a very small fraction of anyone even cares about it, and it doesn't really fix any problem we are facing (global warming, or whatever) or advance some science that makes life better for anyone.
From what I've read I think that for solid instruments, the species of wood has almost no perceptible effect on the sound. More often than not it's some perceived effect that is tied to confirmation bias. Your mind plays tricks on you all the time which is why we have the philosophy of science, logic, and scientific instruments to measure things around to check ourselves.
I do think that heavy/dense vs. lighter woods may change the sound SLIGHTLY. However the vast majority of people won't detect it without confirmation bias coming into play, and your audience (even the player) doesn't know the difference in the mix. There are so many other factors in a bass, like how it's constructed with the bridge and other parts involved.
For example, my G&L basses with the saddle lock bridge have incredible resonance in the wood. Maybe tone wood makes a difference there because of that? I don't know. Many other basses you don't feel the vibration in the body quite the same way, so it's hard for me to believe there is some strong interaction between the strings and wood going on that is changing the tone.
With acoustic instruments I'd hypothesize wood would absolutely have some more effect simply because you are amplifying your sound USING the wood. With electric instruments the pickups are doing that, you don't need wood.