Do other "arts" professions get this sort of thing? Do people walk up to actors and say "how do I get a movie deal?"

From my time in casting -- yes, unfortunately, people do actually ask, "How do I get a big movie contract?"

As a copyeditor or proofreader, I also get asked/told, "I read a lot. So I can do what you do; give me your contacts so I can work for them."

::facepalm::