I'm sure everyones seen a movie where 2 champions or heroes square off against each other in trial by combat during the middle of a battle where everyone just kind of stops the killing for 5 minutes to watch.
Did these really happen during the middle of battles in the thick of everything?
Speaking for the Ancient Greeks here, the answer is maybe, but it didn't work. The outcome was never accepted. The time of the Persian Wars saw the last examples of champion combat. By the Classical period this aspect of military culture was abandoned.