There is a difference between manually shaping a chair leg with a spokeshave, and using a lathe. I consider one "by hand", the other machine asisst.
All CNC does is automate an existing tool. An automated spokeshave is inaccurate just like a human operated spokeshave. You take say an existing 5 axis mill, add belts and motors and automated control. It was an accurate tool to begin with, now it is automated. Or a lathe, or welder, or whatever.
A trained, skilled machinist can match a CNC machine, IF they are basically using the same underlying 5-axis machine. The human is no match for CNC in the speed dept though. You could get a small mill w/o CNC and do extremely advanced highly accurate shaping, just at low production.
After a while, the tolerances don't matter anymore and you've hit a point of diminishing return.