I’m actually doing that - shredding Chewy, Amazon, etc. boxes with a 16-sheet microcut shredder from Costco, and using it to bed a stall and a 3’x12’ chicken coop (also in the barn) for the winter. We probably have about 3" depth in each, maybe 4" in the coop. Note our horses and llamas live outside, so the stall is just used for occasional housing – llamas overnight when they’re wanted the next day, a horse generally for an hour or two except my mare was in for 2 or 3 days with an abscess last month. So we don’t need to replenish bedding regularly.
We are using the stall as an indoor run for the chickens this winter (a covered run is on the list of next summer’s projects) and they seem to enjoy scratching in it. So far the chicken poop isn’t prominent enough to impact the use of the stall for horse or llamas when necessary. We’ll see what it looks like in April. (Northern NH - I hope the lawn will be open & dry for the chickens to go back out to their tractor & poultry net in early May.)
I mostly just shred brown cardboard and newspaper because I spread our stall cleanings on the back part of the lawn and white & colors really show up and look sloppy - a complaint (sloppy-looking fly-away bits from the manure pile) I’ve heard from those who have tried white paper.
My husband complained about the absorbency relative to pellets, but I find it comparable to the sawdust I used decades ago - the urine spreads out a bit on the floor before being absorbed into the bedding, but it is absorbed. It tracks a bit into the barn aisle, but not horribly.
If I were cleaning a stall daily then I think the logistics of creating enough bedding would be overwhelming. But - at least so far - it’s working great for my use.
I’ll attach picture of the coop bedded in the cardboard; I don’t have any of the stall on this computer.