I have no idea why the taper is there. Fleeting is the only thing that sounds logical. Also, not everyone wraps the cones, except the final outside capstan ofcourse.
I actually find wraping the step cones as a bad practice ( draw machines are designed to slip, period. ). Unless, the draft is higher than 18% Ar and your running 20 awg or less.
Everyone has their own idea on what should be. Unfortinately, the manufacturers of the draw machines have been doing the same thing for over 50years, making machines. Us ( the wire manufactures ) make wire. The typical draw machine has not changed mechanically ( it does the same thing, the same way ) it has done for over 50 years. On another note, some draw machines with tapered capstans have traversing die boxes. This would rule out the notion that when the machine is at speed that the wire line stays in one spot on the capstan ( ofcourse it will go back and forth ). I just have no idea why the some capstans are tapered. I can tell you that not all step cones are tapered and function identically the same though.