Yes, agreed.
Maybe the key to that is one or a combination of:
1) Nutritional-- depends what is or isn't in the food you're offering.
2) Behavioral-- whether you can get the fish to accept what you're feeding or, alternately, can find a food it accepts (the wood eating version of getting a fussy carnivore species to accept commercial foods) or whether a shy or nocturnal species is successfully competing for food with other fish in the tank. If an individual of a wood eating species failed to do one or the other and did poorly, without testing their conclusion someone could think it's the lack of wood, without considering other possibilities.
Typically, bottom feeding aquatic species will eat any foodstuff that is available. Their guts will sort out the nutrient content.
This is precisely why bottom feeders such as the wood eating pleco species have evolved under some of the most nutritionally harsh environments. I’m quite certain that mbuna can glean nutrients from algae, yet we all know that this group of fish, that in nature are very specific in diet, can be successfully kept in captivity without so much as ever seeing a strand of algae. The results of several decades of keeping certain species, prove that point. No need for more studies, or more data.
I’m ok with making assumptions based on several decades of observation, my own included. But I also don’t have the analytical scientific type of background that you have. And I say that with the utmost respect. I love science, but I’m also big on first hand observations, mixed with science, especially when those observations are based on many years, and many test subjects. Not enough to author a peer reviewed paper like the folks linked to in this discussion, but enough raw data to satisfy my needs, and to start this topic on MFK.

If nothing else I got members here contemplating the possibilities.
And yes, what one feeds a fish in captivity, be it algae, wood, or otherwise, is most definitely going to determine at least some of the overall outcome with regards to the health of a fish. In captivity, with all other things being equal, I personally don’t see a lack of wood as playing any major role in that equation.