I've never made any claims on annealing other than the seating force or neck tension becomes more consistent. I am not positive my AMP Mark 2 anneals the shoulder hard enough for any gains and no means or the will to test it.I'll go against the grain here...
I have an AMP Mk2 and anneal every firing. I've seen literally no change to my SDs after I started annealing with it, and I'm a few thousand rounds in. In fact, the only change I can see from annealing is at the bench (my shoulder bumps are more accurate, and seating feels more consistent). I haven't seen any increases in my X-count.
I find it really interesting everyone comes in here saying their SDs are way better, because that's not been my findings, nor Litz's for that matter (although I take issue with certain parts of his testing).
But I have to say you do go against the grain. If your shoulder bumps are more accurate, and the seating feels more consistent, and now you can trim each firing making necks the same length also, and you are not seeing any gains in the numbers categories or results downrange, something is wrong. To me, it would seem impossible when you make things more consistent that there are no perceived benefits.