I could see doing it for the novelty once or twice, to see how it responds to certain statements and such. I'm sure people felt the same way about Eliza. I can't imagine doing it for more than that, other than for specific goals like you mentioned. Now, I've never done the first and rarely do the second except as a prompt for a search engine, and most of my searches wouldn't be considered a typical AI prompt, unless you're Jean-luc Picard.