Still a mystery for most of us then...
I thought of the cabin pressurization, but as mentionned, any lag would make the computer to adjust the profile with a repressurization segment.
It seems that the FCOM description is far from complete...but that's old news!
Is it possible that the N1 above idle has anything to do with the Handling of Bleed from the compressor, e.g. to reduce the chance of flow separation or something, as air density is much less at higher levels? Just a guess.
Flex