Mice: fast, common, and confined to soft goods
Mice are the pest most likely to actually damage a storage box, and the mechanism is entirely mundane: their incisors grow continuously and must be worn down, so a cardboard box is simply an easy, always-available target. Extension sources describe the result as clean-cut entry holes roughly an inch and a half across, along with shredded paper and fabric repurposed as nesting material, and droppings and urine contaminating whatever the mouse settled into.
The practical upshot is that this damage is real, routine wherever mice have access, and entirely confined to cardboard, paper, and soft-sided storage. It doesn't touch hard plastic totes, metal, or the storage space itself — which is why switching containers is such an effective, low-effort fix.

