Love that idea! hopefully the rabbits do not chew it away, sometimes they do sometimes they don't.
They do chew on them, but they're free and I can get as many as I need whenever I need. So it's fine.
Some rabbits will leave a nest box in tact for months, some break them violently as soon as the kits start leaving the nest. I like to think of it as enrichment. The ones that get left in tact but are messy get emptied and turned on their sides and used as hidey holes and jumping platforms for the adult rabbits and grow outs. Eventually they disintegrate too into the bedding, usually torn apart by the adults, and then they get taken to the compost when I clean the cages.
Also this means I don't have to sanitize the nest boxes ever, or worry about disease really. The boxes can be composted when they are done being used and I can bring in new, clean ones constantly that have never been in contact with a single rabbit, ever. It's a system that works really well for me.