I’ve pondered the same before. I’m guessing it must be because of the amount of handling, heating, bending and trimming involved for headstock bindings. Which would destroy or compromise any stain that was pre-applied.
On the other hand if you were to stain only after the binding is installed, it might not be possible to use any taping/scraping technique to prevent the stain bleeding into the headstock veneer and neck.
Perhaps only for the fingerboard it might be possible, if you could glue in pre-stained bindings onto the fingerboard before fretting and installing on the neck. In this case the binding strips are straight and may not require so much forming and trimming.
It’s just a wild guess in the end, no one outside of PRS really knows. A luthier would be able to give an accurate opinion!