If you are separating lots by standard deviations you are likely already processing 2/3-3/4 of the brass anyway.
It costs you time unless you have someone else do it for you.
Your processing, trimming, turning, and pocket uniforming all change the weight of the brass. If you sort by weight before doing this it is going to change the result of the sort.
This tech article supports weight sort after material removal.
Hunters care if the brass is turned 1-2k off? Doesn't neck turning improve the results of a load developed with any brass? You would be doing them a favor. A standard full length die over sizes brass drastically and can work consistently for any realistic neck thickness.
Its not my guide. I did not produce it. I posted it as supporting evidence of a single point. Consistency of internal volume measurements improves with firing and sizing.
I hope you are just having an off day. I'm not going to fault you or think different of you for this single interaction we have had, nor do I want others to.
I hope you have a nice Christmas with your family and good luck shooting.