All players, regardless of position, should wear a cup. Yes, that includes the outfielders as well.
When my son was on a travel team, during practice one evening the coach was hitting fly balls, line drives to the outfield. One of the outfielders misplayed a line drive and everyone clearly heard the ball hit his cup. That ended any argument for not wearing a cup for the outfielders.
Another odd story. Travel team is playing a tournament at a 4 field complex. Coach is coaching 3B. From the neighboring field a foul ball hit the coach right on the top of the head. He had a headache for the rest of the day. Made the case for wearing a helmet while coaching.