On a conventional compound leverage press ram, the handle is rigidly mounted to a toggle that is suspended on pivots between the end of the ram and the linkage arms. Since the linkage arms pivot at their upper end, on the press frame, they cannot resist angular forces on their bottom end, where the toggle is. That leaves only the press ram to resist those lateral forces.
Where do these lateral forces come from? From the operator's hand's pressure on the handle. At the top of the handle stroke, you pull the handle towards you and downward. At bottom of the handle stroke, you are pushing the handle away from you and downward. So somewhere in between there is a reversal of the lateral (non-downward) force applied to the handle. The ram is the only part that can resist that lateral force, therefore the lateral force on the ram also reverses.
A second reversal also happens when the line that passes through both pivots on the toggle passes through horizontal. On different presses, this occurs in different locations in the stroke, but it reverses nevertheless, and unless the handle is at a right angle to that line through the toggle pivots, (and it isn't on any press I'm aware of), then these two reversals do not cancel out.
By contrast, the co-ax handle pivots on the press frame, not a toggle tied to the "ram". The co-ax applies rearward and upward pressure on the guide block/rods (the "ram" on a co-ax) throughout the downstroke of the handle. Then for the entire up stroke of the handle, it applies forward and downward forces on the guide block/rods. These reversals (which also occur at the ends of the stroke on a conventional press ram, in addition to the mid-stroke lateral force reversals described above) occur as the "ram" stroke is reversed, pressure on the shell-holder/cartridge/die is momentarily zero, and all three are free to re-align. The mid-stroke lateral reversals on a conventional press ram occur while the shell-holder/cartridge/ram are under considerable pressure, which then allows friction to resist any re-centering.
Many experienced reloaders follow the old addage to pause and rotate the cartridge at intervals during the sizing and/or seating stroke. I wonder if that has more to do with simply the pause (and subsequent release of pressure and re-alignment), and not so much with the rotation.
Andy