looks to me like a simple turret lathe would be just as fast. 1 spindle or 2 dozen spindles the parts still have to be loaded 1 at a time.
A rotary multi station spindle with several secondary spindles and tooling holders might be able to preform many machining steps at once but the whole thing has to stop for a single part to be changed each time a part makes it through the last station. And then just as with a multi tool posts turret each tool must be set for cut depth.
if it drops in a new blank automatically I might be able to see it. industrial screw machines have been making screws without the aid of CNC since their invention