Great idea for extra seating/storage. I would staple the fabric to the wood instead of using a glue gun, and Make a second piece of wood that fits into the crate, and nail it to the first piece on the bottom to keep it from slipping. Then you could really store stuff in it. Kids room? Dorm?
Also on these boards
DIY Milk Crate seats.. Cut a piece of plywood to fit the opening of the milk crate, cover with foam and batting. Place fabric on top and staple the excess underneath the plywood. Place on the opening of the crate.