With the CHIBA system, the free radicals formed during the H2O2 development are not able to crosslink gum arabic in sufficient time, or at all.
Speculating:
The CMC addition is likely inhibiting the dissolution of gum arabic possibly by complex coacervation - essentially the two colloids binding to each other. Since CMC will crosslink somewhat in this system, it seems to grab on and hold the gum arabic. I have found that this indirect crosslinking approach is vulnerable to long rinses, and the complex can re-dissolve and wash out the image. Using gum arabic in the CHIBA system remains dicey.