As far as I can tell, there is no reason why I shouldn't make a box out of eggcrate (plastic grid used to diffuse lighting), sew a square bag out of weed-blocker fabric, and put the bag around the box. The eggcrate would be a form to keep the bag stiff and standing up, the bag would keep all the dirt inside, and it could be made in practically any size. It'd be a bit like those grow-bags, but sturdier and custom-made. Plus, more aeration than a plastic pot. It might lose water more quickly, though, since the fabric wouldn't keep much moisture in.
I'm assuming no one else has done this, but has anyone tried CPs in grow bags?