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
Interesting information describing a Co Ax press's stroke. One of the first things I learned from experienced reloaders 40 years ago, was to loosen the keeper spring holding the shell holder to the ram, leaving it barely any "keeping" ability, and able to let the case float a bit to self-center...as long as one didn't get impatient and try for a sizing speed record and ram it home hard and fast on every stroke. And yes, part of that trick was to pause a second as the case was started into the die. Don't remember any "rotating" advice, except if the case holder was a bit loose, vertically, on a small diameter case...which could wobble and miss the hole by a tad. Newer case holders IME have been a little tighter. Anyway, case concentricity improved hugely just doing that. Ditto for seating bullets.
I agree with your assessment, "more to do with simply the pause (and subsequent release of pressure and re-alignment)" The loose shell holder facilitated that alignment more than any minor lateral ram movement.
I don't care if you have a Lee, Redding, Dillon, RCBS, Hornady, or Forster, the machining and tolerance goals are a lot less than perfect, for perfection we'd be paying thousands for a press instead of mere hundreds of dollars, and I doubt concentricity in loaded rounds would be enough better to justify it.
That said, the Forster/Bonanza Co-Ax design does have some neat features, if you can get used to the high-handed stroke, and can afford the price. I wouldn't mind having one...but using a progressive now for most of my reloading, sorta put the skids on adding any more single station presses. And really, the R. C. has done everything I've asked of it really, really well for 40 years. My R.C. loaded ammo has continually shot better than what's stocked commercially around here, and that's why we reload, isn't it?