I have always assumed that this is to make sure it really is you that is getting on the aircraft. Just because your docs were checked earlier doesn't prevent you from giving your boarding pass to someone else afterwards so they can fly in your stead.

FWIW at many European airports flying between European countries (both in Schengen area and across the Schengen border) I have not been asked for any ID when boarding the aircraft and have felt a bit of a fool offering up my passport only to have it ignored