Rat , I think it's all tying in the floor /wall with the reinforcing strips ... actually they're Very important , although one might not think so ... For those so worried , you could use an extremely Heavy canvas for the bottom outside Reinforcing strip , glued well up onto the sidewall and floor ... wood strips /metal might be "overbuilding" ... Offroad , maybe not a bad idea !!! I think for the bottom to sway , the top has to also .. The rigidity of the Unibody structure should prevent that ... I believe we're talking about "normal" road use , not bumping over some rocky mountain pass ... No Bears either
Eagle , the wood inside would give you a chance to use some decorative paneling on the walls ... Some folks just like the look of wood inside ... can't blame them ... It does look Nice and would add more strength !!! I do think you would need to pre install some "hard points" first under the paneling for attachments, and for those that must , small channels could even be routed for pre-wiring before the ply goes on (lights and stuff) .... Many possibilities...
And since we've practically eliminated most of the heavy bits , the weight of a little wood wouldn't hurt anything ... maybe stop that trailer from rattling

only thing is , the more wood we use , the more we have that old TD problem ...potential Rot ... so all wood used should be well "protected"... all a compromise ... many ways to build it ...