Jim Lewis of eMachineShop also tried to do the same thing for printed circuit board design and assembly. The result was Pad2Pad, which would make blank boards and put the parts on them. The assembly part didn't work out commercially, and the board-marking service became one of many such services. Making PC boards is a well-organized industry - you send in files and get boards back without much difficulty. One-off boards are no problem.

Seeed Studio in Shentzen finally got the assembly thing working. They make blank boards and will put parts on them if you pick the parts entirely from their Common Parts Library. You can make most simple digital electronics projects using that library - analog and power, not so much. Seeed Studio has good prices but requires you to release the rights to your design, so others can copy it. Sort of like Github for hardware.