The language of "generator that stochastically produces the next word" is just not very useful when you're talking about, e.g., an LLM that is answering complex world modeling questions or generating a creative story. It's at the wrong level of abstraction, just as if you were discussing an UI events API and you were talking about zeros and ones, or voltages in transistors. Technically fine but totally useless to reach any conclusion about the high-level system.
We need a higher abstraction level to talk about higher level phenomena in LLMs as well, and the problem is that we have no idea what happens internally at those higher abstraction levels. So, considering that LLMs somehow imitate humans (at least in terms of output), anthropomorphization is the best abstraction we have, hence people naturally resort to it when discussing what LLMs can do.
A lot of the issues I'd have when 'pretending' to have a conversation are much less so when I either keep things to a single Q/A pairing, or at the very least heavily edit/prune the conversation history. Based on my understanding of LLM's, this seems to make sense even for the models that are trained for conversational interfaces.
so, for example, an exchange with multiple messages, where at the end I ask the LLM to double-check the conversation and correct 'hallucinations', is less optimal than something like asking for a thorough summary at the end, and then feeding that into a new prompt/conversation, as the repetition of these falsities, or 'building' on them with subsequent messages, is more likely to make them a stronger 'presence' and as a result perhaps affect the corrections.
I haven't tested any of this thoroughly, but at least with code I've definitely noticed how a wrong piece of code can 'infect' the conversation.