I just got am email from PCB directory full of PCB industry general news. What struck me was three articles on CNC PCB prototyping. It is looking tile there a re quite a few very specific PCB prototyping CNC machines nowadays e.g:
The lab I worked in had one about 20 years ago. I don't remember the brand, but it was basically just a very small CNC mill, there are probably a lot from the hobbyist CNC market which could be used. The "pcb specific" part was essentially the software to go from Gerber files to the CNC paths (you have an image of the positive, the copper you want to keep, but you have to generate the cut path to remove copper, so kind of a specialized work flow at the time).
The primary selling point was that you could churn out something to test in a day, as opposed to waiting on a quick turn PCB house to get you something in a week for a high price.
That is the upside.
The downsides aren't hard to figure out:
You don't get plated vias, so double sided boards are tricky to build, assuming your setup is precise enough to keep top and bottom aligned;
You don't get soldermask or tin plating, so the boards start to oxidise really quickly, you have to go over the board with some fine emery paper or something similar to shine it up right before you build, and you proably want to spray the whole board with conformal coating afterward if you don't want to have copper oxide slowly diffusing into your traces;
No silkscreen, so you have to double and triple check component stuffing anywhere the board gets very dense, and it is hard for someone to double check your work compared to scanning over a board with silkscreen component designators.
Given how cheaply you can get double sided boards with soldermask these days, I think the time argument is still the only one that makes sense, by the time you figure in machine cost and your time the cost saving argument is hard to buy.
If you have an idea you really want to check out before the end of the week rather than waiting two or three weeks to get PCB's delivered from Hong Kong or wherever you either have to hand etch, or mill. At least with milling you don't have a bucket full of nasty chemicals to dispose of after.
Having the ability to make precise size traces and spaces is useful if you need impedance controlled prototypes for high frequency work, which was why we had one in our lab, but for analog audio I think it would probably be easier to build a proto by hand with wires and then get factory built PCB's a few weeks later.