So imagine you make the depth of the toaster greater than the height (easy with those feet). You put a quarter inch radius on the top plate, make the front and back plate a half an inch shorter so they nest inside the top plate in the box. And in fact if you put locking tabs on the two plates to keep the front from oil canning, those would also fit in if you flip the plates the right way 'round in the box.
You can tell from the bolts in the picture that there are already right angle bends in the sheet metal. So they're already using the third dimension just not with as much flair.