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I think it’s a fun technology, and can see the attraction from the point of view of a hobbyist or someone who wants to live a more DIY lifestyle than most. For me, it’s nice to be able to prototype quickly. Getting usable machine parts requires more time and effort than standard machining, though.

My daughter contributes time and skill to an international charity project that designs and prints 3D prostheses for use in third world hell holes. The parts need nothing more than a sandpaper touch up before being assembled with simple hand tools. That is part of the design. An additional feature, and one that is more to your point that "Anybody who’s handy enough to get real use out of a 3D printer and has time/space for the project, can make a DIY CNC vertical mill or lathe that will produce high-quality parts for about what they’d pay for a good prosumer-level extruder."
is that the skills needed to run a 3D printer are significantly less than the skills required to run a manual CNC mill and for a few thousand dollars a site can be set up in a third world slum that provides real benefits to the local population without having to have skilled machinists onsite. One doctor, one low-skilled technician and voila, artificial hands, feet, arms and legs, custom fitted to the patients' needs, are going out the door. Cool stuff and being done today.

"the skills required to run a manual CNC mill"

I wasn't talking about "manual" CNC (computer numeric control) mills. You can build one (with software control similar to 3D printing, minus automatic bit changes) for a couple/few thousand if you know what you're doing. Yes you would need some expertise/skill to source parts for and build the CNC mill.

For prostheses, 3D printing is the way to go for weight savings and relative ease of producing complex infill patterns especially for one-off parts. There are a few niches where 3D really shines, and medical prosthetics are one of them.

I doubt it's anywhere near as "low skill" an endeavor as you believe. Possibly somebody wrote and supplied a software package and equipment which makes them able to take a 3D scan of the patient's body and produce a model to print? Or qualified biomedical engineers and doctors spent numerous hours developing 3D-printable universal prostheses in conjunction with the company that produces the printers? That takes considerable technical know-how to pull off, and possibly a good bit of money that isn't included in your costing. This kind of support would probably not be available free of cost to a typical consumer or business in the 3D printer market.

For 95% of typical machine parts, the printers commonly sold as consumer/prosumer models for under $10,000 are less useful than CNC mills because it is impossible or nearly so (at least from what I've read/experienced with current models) to correctly place and dimension clearance/dowel holes and tap bores with the kind of precision that demands. And as you said yourself, 3D printed parts require touch-up after printing. In the case of machine parts where you must have things like perfectly flat or round surfaces and precise alignment for parts to mate correctly in complex mechanisms, they require considerable touch up. They often require the kind of "touch up" you need a vertical mill or lathe for. They require enough touch up that parts are at least as time-consuming and expensive to produce as they would be with subtractive methods. They take an added layer of skill/expense, because you still need to to do some basic machining on top of having a printer and being able to get relatively good results out of it. Add to this that you will not get the full mechanical strength out of the material. It currently takes considerable skill, effort, and expensive software to design around this in applications where a part might be stressed near failure. In some cases (like gunsmithing) you'd have to have a screw loose, or be in a pretty desperate situation to even bother trying.

That's where the affordable 3D tech (extrusion and low-end SLA) is currently at. I'm not saying they're completely useless, but they're limited unless you have alot of time on your hands and access to other tools/equipment. The other tech (high-end SLA and SLS) has not budged in price much the last 3-5 years. It's currently way out of the "consumer" price range. It may come down to earth at some point, or it may not. We'll see. Some of the patents on those technologies expired a few years ago, but they're not easy to reproduce from a technical standpoint. Alot of the individual components which make them capable of doing things like fusing powdered metal to within +/- a couple microns are expensive in their own right even without the development costs and markup.