It would be nice if we could get an LLM to simply say, "We (I) don't know."

I'll be the first to admit I don't know nearly enough about LLMs to make an educated comment, but perhaps someone here knows more than I do. Is that what a Hallucination is? When the AI model just sort of strings along an answer to the best of its ability. I'm mostly referring to ChatGPT and Gemini here, as I've seen that type of behavior with those tools in the past. Those are really the only tools I'm familiar with.

LLMs are extrapolation machines. They have some amount of hardcoded knowledge, and they weave a narrative around this knowledgebase while extrapolating claims that are likely given the memorized training data. This extrapolation can be in the form of logical entailment, high probability guesses or just wild guessing. The training regime doesn't distinguish between different kinds of prediction so it never learns to heavily weigh logical entailment and suppress wild guessing. It turns out that much of the text we produce is highly amenable to extrapolation so LLMs learn to be highly effective at bullshitting.