What is the economic value of all these AI chat logs? I can see it useful for developing advertising profile. But I wonder if it's also just sold as training data for people try to build their own models?

Pretty easy to match up those logs with browser fingerprinting to identify the actual user. Then you have "do you want to purchase what Mr. Foo Bar is prompting the LLM?"

Not just advertising but market research. Loads of people want to know exactly what type of questions ppl are asking these chat bots