Isn’t there obvious problems baked into this approach, if this is used for anything but fun? LLM’s lie and fake facts all the time, they are also masters at enforcing the users bias, even unconscious ones. How even a professor of history could ensure that the generated text is actually based on the training material and representative of the feelings and opinions of the given time period, not enforcing his biases toward popular topics of the day?

You can’t, it is impossible. That will always be an issue as long as this models are black boxes and trained the way they are. So maybe you can use this for role playing, but I wouldn’t trust a word it says.