One element they provide that co-op narratives do not is the element of randomness. The Game Master (the person who knows the basic elements of the story and represents all the non-player characters the group encounters), has the power to alter the die roll but should do so sparingly and secretly. When players detect dice fudging they often lose respect or push the limits and abuse the gesture.
Having statistics to represent a character's abilities allows everyone to determine their character's exact potential, rather than leaving it up to who can pontificate the greatest.
The narrative side of the gameplay is not lost, however, because the players are encouraged to speak in character and to describe actions along with rolling their dice. Situations where the player would not have the mental capacity to narrate, the dice speak for themselves, without much talk- disarming a bomb for example. Sure my secret agent would know how, but I don't. I roll my explosives skill and let the dice do the work in this case.