One major constraint in making 3D printed wooden furniture is the size of the parts which is too large to be printed by most of the 3D printers. So the solution is computer program with an algorithm which can take any 3D model and convert it into foldable pieces which can be assembled to get the furniture. Unfortunately it is beyond human level of thinking given a large number of possible orientations, dynamic shape configurations and spacial reasoning. Here individual parts can be easily printed as they are of smaller sizes in large numbers.
Since the furniture is foldable it is easier to ship and makes the furniture mobile which adds value to it. Also the furniture itself is customizable people can add and remove slight modification to designs and print it at their home and assemble. So if a furniture runs out of fashion then users can tweak some parts in the furniture to make it to a new design again.
Making something like this with traditional carpentry will be very labour intensive process but with 3D printing in wood it become very easy.
With a bit of research it may be also be possible to make the entire foldable furniture as a single whole print rather than making it in parts and assembling it.