1) Warm up occurs. Out of the box from the back of a car/warehouse/delivery truck won't sound the same as a device that has made its home in the living room and been running a bit before listening. This will also affect mechanical parts, whose rigity and dimensions will change slightly with temperature.
2) Your head getting used to the sound produced in the environment the hi fi is placed in occurs.
Those two changes alone are really going to get in the way of hearing actual burn in.
Moving parts changing as they go through their range of motion repeatedly does occur. Speakers most notably fit here but they will also likely be most affected by 1).
Valves characteristics can change over their lifespan.
I am tempted to class clocks as a moving part, but only from my own listening. To me some clocked devices change over time and they do the same again when their clock is replaced. Some clocked devices have been the same from day one though. It isn't easy to tell if this is true due to 1) & 2).
The rest of the electronics. No.