The point of making a machine from scratch means there's no donor machine needed. So no testing of the parts that do and don't work, and no having to source a machine, which as years go on will be less and less easy, and possibly more and more expensive.
Each VCR from what I've read has its flaws, from 'things that always break' to being a pain to work on due to the way its constructed. This would be a chance to make something that is more easily serviceable, and also broken parts can be reprinted rather than looking for yet another donor machine.
As I guessed, the heads seem to be the fly in the ointment. What sort of precision are we talking here? There's already a printing that can go as fine as 6 micron (0.0006") in plastic:
http://www.incept3d.com/high-resolution--objet.html
Remember I'm not expecting this could be achieved today or even next year, but we seem to be getting quite close.