They all come in handy when I'm looking at an upcoming season and wondering what to use for an audition. After a moment's thought, I go, "oh, right--I have that."
What I don't have are enough monologues to cover my weaker areas, but the two or three I do have for them, will get me by.
Monologues do not demonstrate talent, but they do demonstrate readiness to do the job. Can you begin, middle, and end? Can you move well, speak with clear diction, make sense of the rhetoric (in both classic and contemporary pieces), inhabit style, demonstrate a craftsman-like attitude? Monologues are valid (if not necessarily sufficient) tests of these skills, which don't take long to become visible or not; 30 seconds is often enough (any of the literary people I know who have coached writing or judged writing contests will recognize the truth in this: how many short stories submitted to a contest make clear their writers' skill in the opening paragraph?)