Reflecting on this now, I can see that it was a bit of an odd way of looking at things. What it may have prevented me from initially doing, however, is recognizing the importance of stock characters in a drama, and how central they were to the tradition of the theatre when it was reawakened in Europe after its centuries-long slumber.
Perhaps studying Dario Fo's Accidental Death of an Anarchist has reminded me again of the tradition of mystery, miracle, and morality plays so important to Western drama, the hints of which you can see in the plays of Shakespeare (Egeus, for instance, in A Midsummer Night's Dream or Hotspur in Henry the Fourth, Part I quickly come to mind). The latter play makes far more sense, in fact, when you understand the theatre that preceded Shakespeare.
So the other day I decided that I would give stock characters their due. I asked students to choose such a character from Fo's play, from either the tradition of Commedia dell'Arte or the medieval stage, or from the history of film (provided that at least three instances of such a stock character could be demonstrated).
Here's what my student, Hannah, came up with. She chose "Il Dottore" from the tradition of Commedia dell'Arte:
I think there's a definite usefulness in doing this activity in advance of studying a unit on drama and posting the resulting work around the room. That way, when your students encounter a character who seems two-dimensional, they have a visual repository to draw on that will get them up out of their seats and scouring posters of "Il dottore" or "The Vice" or even "The Rebellious Teenager"
I'd love for you to try this activity and send some examples of what your students come up with. I'd be happy to feature them on the site!