Brass thickness moves up toward the mouths. The donut area will grow in thickness, and eventually you'll be trimming at mouths.
The case with high headspace will stretch back to the bolt face on firing. This will cause thinning at a point low on the body where the case finally did not have enough grip with chamber walls to prevent the stretching. Then when you squish that stretched case back into proper head spacing, you will move brass thickness up the case (not into the thinned area), so that thinning cannot be restored to normal.
Cases taper in thickness from webs all the way to mouths. Notice that your sizing actually begins low on the case, moving upwards. This rolls brass thick toward thin, near webs all the way to mouths.
This changes cartridge character a little bit with each cycle, and these changes cannot be countered with the same process that creates them.
So unless it's in your plan to accept this change (through sizing and/or replacement), then it's best to minimally size.