At one point there was a push to get rid of company watches.... they really don't do much, until the great CO leak in 2nd battalion. The company watch standers were credited with saving all of 2nd bat... not sure how they really detected the orderless, tasteless death gas.... but none the less your job as company duty midshipman is to save the day from stuff like that... not sure how... but yeah... go on tour and do stuff.
I always thought the purpose of standing those BOOW watches and others was to get used to standing watches at sea. . . . do they still do the dock watch (my personal favorite).