Why the crown often is positioned at 3 o'clock

The common explanation is because then you can wind and set the watch while you're wearing it.
That explanation can have some kind of sense to it, but I don't think it's the full story. From what I've observed, most people actually remove their watches from their wrists for winding and setting, and seen that way it's clear the crown is where it is so you can manipulate it with your right hand, not because the crown is accessible when the watch is on the wrist.
This also means I don't think crown position is any reason to wear a watch on either the left or right wrist. Unless it digs into your hand, of course.