A great reason why 3D printers make sense... because you don't know whether your concepts are going to work in the real world. A case in point is the design for a coffee hopper - shown in the video below. The idea is to create a hopper which will hold a dose of coffee from the grinder and release it into the puck on demand.
This design looked like it made sense, with just a single flip dropping the dose. So it was a click of a button to download the design to the 3D printer to try it out. The result is here; the two pieces fit together straight out of the printer and worked mechanically just as in the design model video.
So; back to the drawing board. Cost of trial print - $2. (And of course the design time.)
A great way to try out ideas before committing to a final device.