Lathes were powered by hand, or foot, so if you're going to allow a drill press then you have to allow a lathe.

Files, hammer, and punches are tools, but so are machines. That's why they're called machine tools. It seems we've become accustomed to the idea that if something is driven by an electric motor or steam/gas engine that's where we draw the line. Not sure that's an especially meaningful line, but OK.

There is a world of difference between producing a part with manual machine tool and a CNC tool. Those who don't understand the difference have never used the two.