One of the arguments that I have seen put against "running in" is the idea that it always gets better, you would expect some things to sound worst with use. I have heard exactly that taking place, change to a circuit sounding good at first but with time changing and becoming unpleasant so discarded for another.
I have found amorphous core transformers have some very strange burn in properties, I am sure I have heard them change audibly from one state to another in the process of listening to a few minutes music, only seems to happen once, but I suspect it actually happens to both chans at different times but you only notice the second one changing.
I do wonder if just age itself improves the sound of components, and thats part of the reason for the sound of NOS parts, maybe a release of internal stress over time. Though it may be the process takes a lot longer if its not used.