> LLM chatbots ... were not designed to be "factually correct" they were designed to predict words.

For this question, what LLMs were designed for is I think less relevent than what they are advertised for, e.g.

"Get answers. Find inspiration. Be more productive. Free to use. Easy to try. Just ask and ChatGPT can help with writing, learning, brainstorming, and more." https://openai.com/chatgpt/

No mention of predicting words.