Even if training on copyrighted material is considered fair use, there is still the issue that LLMs may reproduce significant parts of the training set. In fact

Even if training on copyrighted material is considered fair use, there is still the issue that LLMs may reproduce significant parts of the training set. In fact, there is an ongoing lawsuit in Germany (GEMA vs. OpenAI) because ChatGPT reproduced significant parts of existing song lyrics, which very likely violates German copyright law. The whole thing really is a legal minefield and some companies do indeed prohibit the use of LLMs for this very reason (until all of these legal questions are really settled).