That's interesting, could you point me to some source on these findings?

It seems to me that the difference between "iterative improvement" as you put it and "close to the identity" (as in the output is close to the input for most of the volume of the input space) as I put it is fairly subtle, anyway. One experiment I would like to see is what happens to the reasoning performance if rather than duplicating the selected layers, they are deleted/skipped entirely. If the layers improve reasoning by iterative improvement, this should make the performance worse; but if they contain a mechanism that degrades reasoning and is not robust against unannealed self-composition, it should make the performance similarly better.