Bully-
I haven't messed with any of the woven carbon fiber material but does it stretch? Anything you put on the back of a bow needs to be able to stretch and then return in order for it to work. Correspondingly anything on the belly must compress and then return. There is a layer ("somewhere") in the middle of the bow stack that is neutral and neither stretches or compresses. The types of backing and belly materials determine where the neutral spot is and it is sometimes not right in the middle.
I think what the guys are eluding to is that a backing material that will not stretch will hamper the performance of the bow or might damage it because it moves the neutral layer too far away from center. Also, if it doesn't stretch when you draw the bow it might just pop off or be wrinkly.
If you are wanting the woven carbon look, take a look at this stuff:
https://vvividshop.com/collections/carbon-fiberI ordered and just received some adhesive backed VViVid vinyl in a desert camo that I will be applying to some limbs. I think it will work well.
OkKeith