I would suspect that is why some chuck manufacturers recommend only using a specific pinion for final tightening and why some individuals recommend a final tightening at all three positions. I would also suspect that better surface finish is one of the reasons why the name brand chucks happen to have better runout specs.
What brand of chuck are you using? If I did that with one of my chucks the jaws would bind.
Buck and Pratt Burnerd.
Since we are on the subject, I have the Buck adjustable 3 jaw, and the generic that came with the PM 1228. Should the Buck see limited use on special projects, and put the PM chuck back on for daily chores?