The big difference between a subtractive (a cnc router or mill) and additive (a 3D printer or embroiderer) is that the path doesn't really matter that much for subtractive, but it is make or break for additive.
Before anyone jumps in, yes, there are subtractive methods (path generation) that generate better finishes and tolerances, but at the end of the day, it's about removing what is not wanted to reveal the final part/product.
It's an interesting topic, I have access to a single color cnc embroider machine at Techshop. While it's nice, the real money makers are multi-color, multi-needle machines. I suspect a DIY single color machine is completely possible. Multi-color/needle could be handled as tools with offsets, the issue is obtaining (or building?) a multi-needle sewing head. Most of the multi-needle machines cost as much as a car.