I'm an experienced board designer, having designed 100+ boards over the past decade, and I have yet to hear a good answer for why the PCB part number is traditionally on an external copper layer, and the PCBA part number is on a silkscreen layer. To me copper is always "sacred" and should not have anything unnecessary on it, as this can screw up voltage isolation, RF performance, etc. But for some reason designs tend to have the bare PCB part number in copper instead of silkscreen. Why?
I do a lot of multi-layer boards and the board reference number plus layer name gets put into the copper on all layers plus, there is a drawing accompanying the job that states the layer stack up to make sure that the bare PCB is made correctly. No chance of screw ups. If there is enough room on the PCB (say with 4 inner layers), there will be 4 distinct places on the board that if you shine a strong light through you will see the internal numbers. You can therefore inspect the layer stack to see it has been built correctly.
I'm not saying that there aren't other reasons but these are mine.
My company started designing PC boards in the early '80s. These were single-sided boards with NO solder mask or silkscreen. The only permanent location for the board number and company information was on the solder-side, in copper.
Even though we now design double-sided boards with solder mask and silkscreen, we still include board number and company info on the copper-side layer. We also include that information on the component-side layer as well, room permitting. And the silkscreen layer, of course.
I asked this same question years ago earlier in my career. The answer I got was that the copper layer usage for the board number was more permanent than silkscreen. In other words it was harder for someone to scrape off the copper number text than it was for someone to remove the silkscreen.
Some of the intention of more permanent board markings, I was told, was to make it easier to see if some unauthorized person or company was modifying your hardware somehow and selling it as their own product. A scraped off copper area on the board would be much more obvious than a silkscreen that was removed by some solvent.