I was pondering the viability of almost exactly this. Could one invest in a hardware pipeline that efficiently combines e.g. 3D printing with FPGAs to create the consumer-electronics equivalent of Lulu.com's just-in-time small-batch book printing + drop-shipping.
Or, in other words: you can do pretty much anything with the sensors in a modern smartphone. All most manufacturers probably need is smartphone boards (with maybe some options of extra sensors) in custom cases with fancy buttons and displays, maybe custom remotes, and a cute little 4-colour double-walled box. That describes everything from Nest to Roku to some drone controllers.
JIT small-batch assembly seems roughly analogous to other low-volume electronics, which are obscenely expensive. For example, specialty bench equipment like spectrometers can cost as much as a house.. There are many factors at play there, but you can bet one of them is very low volumes.
This is why, at least so far, the kind of play you describe is accomplished with large batches of a generalizable platform that can be sold into many different devices.
Happy to make some free parts for anyone's ideas on here!