People often make the erroneous assumption that CNC means inherent accuracy. Nothing can be farther than the truth. Accuracy only happens if YOU care (and know how) to measure it! If you want to manufacture an R8 collet for example, as seen on robenz's videos you need a grinding machine and more importantly an accurate set of gages. To manufacture the gages you will be doing mostly manual work and you will be measuring the hell out of it regardless of the method of manufacture.
CNC is good if you want to churn out many parts with averagely skilled workforce. Then again if you want to churn out millions of parts CNC is no good, you get yourself a good old cam operated lathe (aka. screw machine). If you want plumbing fittings or ammo cases by the million and dirt cheap this is your tool of choice since the beginning of the 20th century until at least the end of the 21st, not even remotely threatened by the advent of CNC machines as they require 4 times more energy and floor space and are slower.
If you need a die for some aircraft fuselage part with crazy compound curvature CNC is your friend. But then again there was no CNC during WWII yet no lack of aircraft, so I might be missing something.
To cut it short
Manual machines - One offs, Repair work, Home shops (I'd go manual for a home shop every day of the week)
CNC Mashines - Small batches 1000 to 10.000 pcs, Complex curvatures, compound surfaces
Cam lathes, Screw machines, Thread rollers, Broaches - Million part batches
Of course all of these machines work on soft annealed metals. After machining most parts undergo heat treatment which is notorious for crooking an distorting parts to ruin any accuracy so far attained. This is why manufacturing people don't fuss all that much about accuracy up to this point. The main object is to remove the bulk of the material and to leave just enough to be machined after heat treatment. At this stage most parts are too hard to be machined conventionally. So the final and most accurate machining is done by grinding and for the ultimate in accuracy lapping and super-finishing.
For any of these you need a full set of measuring tools. If you can't measure it, it ain't accurate.