The old-time single shots, like that Colt Camp Perry model, were made for the slow fire part of match shooting for the reasons Bob mentions. Slow fire is ten rounds in ten minutes, so there is no problem using a single shot pistol if the rules allow different guns in a match. (Timed fire is two five-shot strings, each string in 20 seconds. Rapid fire is the same, but each string is 10 seconds.)
But other single shots have been used for other reasons, like simply having something different.