Earlier quoted context omitted.
I can see why they'd struggle, I'm not sure what you're trying to ask the model to do. What type of analysis are you expecting? If the model is supposed to represent the views expressed that would be a summary. If you aren't asking it for a summary what do you want it to do? Do you literally mean you want the model to perform conversational analysis (ie, https://en.wikipedia.org/wiki/Conversation_analysis#Method )?
Usually I use the format "Analyze the following ...". For simple discussions this is fine. For complex discussions, especially when people get into conflict-- whether that conflict is really complex or not, problems usually result. The big problems are that the model will misquote or misrepresent views-- attempted paraphrases that actually change the meaning, the ordinary hallucinations etc. For stories the confusion…
It doesn't surprise me that you're getting nonsense, that is an ill-formed request. The AI can't fulfil it because it isn't asking it to do anything. I'm in the same boat as an AI would be, I can't tell what outcome you want. I'd probably interpret it as "summarise this conversation" if someone asked that of me, but you seem to agree that AI are good at summery tasks so that doesn't seem like it would be what you want. If I had my troll hat on I'd give you a frequency analysis of the letters and call it a day which is more passive-aggressive than I'd expect of the AI, they tend to just blather when they get a vague setup. They aren't psychic, it is necessary to give them instructions to carry out.