I've always played the games (even those without named characters) as not so much a game about an overall story which features characters, but rather a game about characters which just so happens to feature an overall story. The real stories are those of each character in the game, and I find I enjoy the games much better this way. As much as I detest Tidus, I think he emphasizes this "character stories, not global stories" idea when FFX begins with him saying something to the effect of "This is my story."