There seems to be some misunderstanding about the functions of the various surfaces of a threaded spindle: the thread simply tightens the chuck against the annular surface (aka vertical flat). The annular surface provides precise axial positioning but neither the annular surface nor the thread provide accurate concentricity - this come from the precisely machined cylindrical surface on the spindle.
Yes, there is some misunderstanding - this comment is NOT true. The surface between the threads and the spindle shoulder does NOTHING to register the chuck. Most chucks made for South Bend lathes have clearances here of 0.005 to 0.010". This area is just "the space between the end of the thread and the spindle shoulder".
Lest anyone get angry at this, let me explain:
Take an imaginary and simplified spindle and backplate:
In this scenario, the counterbore has a 0.010" clearance.
Assemble the two:
As they are assembled, the force the spindle is pushing back must be balanced by the force the backplate is pushing forward. During assembly, gravity is making the force per unit area higher on the top of the assembly than on the bottom. Once contact is made with the spindle shoulder, the forces on the top of the thread will continue to move (up, in this instance, as it is the only way it can go) until it is equaled by the forces on the bottom, which are trying to move down (the only way THEY can go). Once equilibrium is reached, both the bottom force and the top force will be the same, as they have fought each other to a standstill (literally). Where do they meet? In the proverbial middle. And where is the "register"? It is now 0.005" off the spindle - exactly where you would expect it.
Now, what would happen if the register would be making contact (at the top, since gravity would insist on this)? That means that the backplate (and thus the chuck) would have 0.010" of clearance on the bottom. If it was machined like this, the machining would remove this error - for this orientation. With the plate machined with this error, once the chuck was removed, you have lost this registration. The only way this registration could be repeated, was if the spindle was in the EXACT SAME position on the lathe (call this point 0º). If the spindle was rotated 90º, the error would start showing itself, because in this scenario, it is the "register" that is registering things and not the shoulder and threads and gravity would enforce its laws. The error would continue to get worse until the spindle was at 180º, in which case the error would be double (or 0.002").
In my simplified scenario, I break the forces into a top and bottom force. In reality, the forces are equally distributed over the entire face of the threads, but the simplification still holds true.
The better the fit that the backplate has to this plain part of the spindle the closer the chuck will be to the axis every time you screw the chuck off and on again. You won’t get a turned thread in cast iron accurate enough for the sort of repeat concentricity that a chuck needs.
You don't need a precision thread here - all the thread has to do is be the same pitch as the spindle and it will push the back plate tightly against the vertical register. And this is repeatable, installation after installation. Sub thousandths runout with clearances in the cylindrical area of 0.010" is not uncommon.
Now if you still
think that the cylindrical area is a register, just think of what it would take to
make it a register. Make yourself a cylinder 1.500" in diameter and a hole also 1.500" in diameter, then try to fit them together. You'll find that it is no easy task. To produce chucks with near a ±0.0005" tolerance hole would greatly increase the cost.
Registers on chucks like the D series and L00 type have tapers for the registers. A non self-holding taper repeatably registers itself with very little runout.