What cockroaches genuinely damage beyond food
UC IPM, a leading university extension source, states directly that cockroaches "destroy fabric and paper products, and impart stains and unpleasant odors to surfaces they contact." That's a real and well-documented mechanism: cockroaches graze the starchy sizing and glue in book bindings, starched fabric, and wallpaper paste in much the same way silverfish do, and their droppings and regurgitation leave dark staining and musty odor wherever they travel repeatedly.
That staining and grazing is genuine cosmetic damage — annoying, sometimes stubborn, but never structural. It's the honest, sourced part of this question, and it deserves to be said plainly without either inflating it or dismissing it.

