What I've done for cardboard construction is to laminate sheets (with regular wood glue)to each other. Sheet were coated with polyurethane to waterproof. I once made a play fort (48" cube with a 1/3 loft) for my daughter using this method. The walls were made as an exaggerated Ibeam (main panel 2 layers & "beams" were 4 layer ) which I found to be rigid and strong. It took a lot of rough housing before she decided that she wanted to be a princess not a tomboy. The corners were built up lap joints that tied the walls together (duct tape was my clamping method). There was no roof (if there had been I would have made a couple spars and laminated a 2" panel on edge). It was easy to sand and paint.
Can't find the picture I'm thinking of but it showed 4 laminated cardboard barstools with a VW beetle sitting on top of them - shows the strength of lamination.
I think the insulating factor is a drawback but the soundproofing it could provide. suppose??? a TD wall height I beam is made of 2 layers, foam sandwiched on both side, fabric , paint??? Cardboard could be cut easily to make arches, bows,etc that might otherwise be difficult in wood.