I'd pay $0.005 per conversation, provided the payment is not inconvenient, anonymous, and an account isn't required. That in my opinion is the root cause of the problem, people can't pay easily even if they wanted to pay instead of get ads.
I think the next natural evolution after showing ads in chat sessions is providing services where LLMs tailor site content to include ads in real time. Right now you get served a prepared advertisement after the bid is won and the ad for you is selected. With LLMs, both the bidding process and the ad served would be seamlessly integrated with the site content/context.
Part of the "problem" with ads is people know they're ads. What if this comment was edited by HN's servers and rephrased to mention a specific product? You might see a sentence about how OpenAI is the future, someone else might see how claude or anthropic are. Another person might see a paragraph from me about how I used Tide to clean laundry this morning with the help of AI, telling me the right portions for the right cloth. You might suspect it's AI but you won't always be able to tell. Even if they made it more obvious like how reddit is doing it, the content of the AD itself, pictures, text,etc.. could be crafted dynamically so that it embeds in your subconscious without much resistance.
The tech developed to make ads more effective is also used to influence people for other purposes. The current state of society came about after the widespread accessibility of smartphones, social media and the rise of surveillance capitalism. Russia's influence ops using ads is well documented for example. I mentioned all this to say how catastrophic the combination of LLMs and advertising could be, even by today's standards.