It has already been touched on twice above, but the whole idea is misguided from a mechanical point of view.
Look at the degrees of freedom of the three parts (spindle, collet and nut) and how each degree of freedom is eliminated.
Think of a lathe chuck that goes onto a threaded spindle nose. The register provides concentricity; the threads are supposed to be loose enough so that they only provide axial restraint. The collet/nut/spindle assembly works in a similar way.
If you tighten up the thread clearance so that it does attempt to provide radial as well as axial restraint, it will fight whatever mechanism is already in place to assure concentricity.
Tightening up the radial clearance of the thread will also tighten the axial clearance and could lead to skewed contact (unequal pressure) between the face of the collet nut and face of collet. You need a (relatively) rattling fit on the thread in both directions so the taper in the spindle is the only thing influencing the collet’s radial location and the face of the nut is pushing it smoothly and evenly into that taper.