The problem with 3d printing is that you need to be precise. Your idea is conceptually good. The challenge is now how do we do that cheaply and precisely. The way I am looking at it, every stage you add to the forklift mechanism will add 2 smooth rods and 4 linear bearings. You can quickly see that the vitamin count will get out of hand. In many cases, scaling up an existing design to get a big print volume is the cheapest solution. The benefit of your idea would be that you could possible make a compact robot.
If you like this idea and want to see it happen, I encourage you to run with it.
If you like this idea and want to see it happen, I encourage you to run with it.