The conventional wisdom is yes in NYC, no in LA. This said, I've had both an agent and a manager ask me for monologues.
Bear in mind too that a lot of film work is very monologue-like - that is, you address the camera and endow it with your partner's presence (even for brief lines). So learning to summon up the richness of a relationship without actually having the person in front of you is still an important skill.
(Full disclosure: in case you haven't been to my site, I have free monologues there and two books of them out, and am working on a third - so I'm not COMPLETELY neutral.

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The other consideration is trying to give agents and CD's what they want. Many will ask if you have a reel - but just try getting them to watch it if you send it. Still, you want to piece one together.
If you're concerned about the one thing to bring to these folks, it's flexibility and confidence as an actor. Working on monologues is one way to build that, as is doing improv, scene study, etc. I would think of it as one tool a rounded actor should have, but more because you want to be a rounded actor than out of concern for what CD's and agents want. Other than strong, professional actors, I don't know that they know themselves. Until they see it.