I have two presses - a Rockchucker Supreme SS and a Lyman T-Mag II turret press.
RCBS replaced the ram in the RC. The slot for the shell holder was not centered. All OK. And the ram is solid and has no or little slop.
The Lyman handle and ram have a lot of slop by comparison. I have read that this can actually aid in centering the case during sizing and bullet seating by allowing the ram to align to center the case in the die, and it is possible a rotating die holder requires greater tolerances. But the slop bothers me even though I only use the Lyman turret press for pistol ammunition, and then mostly plinking ammo. It probably makes no practical difference in the quality or the target (in my case). (The die holder itself does not move - the support in back is fine.)
Is there any harm or benefit in fitting brass bushings between the handle, linkage, and ram, to remove some of the tolerances?