Here's a reply from the low-tech practical experience end of things.
We've built lots of buildings here in the Indian Himalayas (Ladakh) with what I guess should be called either "formworked cob" or "packed earth" without any organic material, and also some with wood shavings and sawdust.
The plain cob, a mix of sand and clay (actually technically silt but it worked fine) made very strong walls that hold lots of weight, have survived 20 years just great, have proved to be almost as hard as concrete to break when needed, and do reasonably well when built out in the elements without cover or plaster.
In the past 5 years we've also made some walls for more insulation, where we mixed a lot of wood shavings and sawdust in. Straw is not a waste product here, it's fed to cows, so we didn't have much straw. For a room to hold our
water tanks above freezing, we made the new north and west walls out of form-worked packed cob with a hefty mix of the only organic material available as a waste produce here, wood shavings and sawdust from the
local lumber yards. It is distinctly less strong than the plain earth mix, but since it's a low roof, a small span, and nobody sleeping under it, we don't mind. It was left unplastered for 4 or 5 years, and was pretty crumbly; if a person stood next to it talking and idly digging with a finger, a bit of damage could be done, though it did eventually reach a tougher layer inside. We finally plastered it last year, so I guess that will help with this kind of erosion.
We also made 2' x '1' x 6" bricks out of a similar material last year and made the three outer walls of a new
solar house. Since the wall is 2 feet thick, has a concrete tie beam above, and the house is only one story, we're using it as a residence, with people sleeping underneath.
I don't have a conclusive
answer for you, except that in my experience, adding sawdust and wood shavings makes a wall less strong, not more.