There is one thing I found to be true over and over again no matter what the anchor point is for the conversation, no matter the context, no matter someone’s sentiment, etc: nobody likes to have their time wasted.
LLM’s are incredibly useful for cutting corners. It makes it very easy to waste people’s time. No matter how useful they are, no matter the use case you have found, no matter the integration, people keep encountering bad search results and people sending them clearly LLM-generated work that wastes their time.
Unless somebody comes up with a cure for that, there will always be a significant portion of the population that is hostile to LLM’s - and rightfully so! No promise of productivity will overcome that.
TL;DR: the biggest problem with LLM’s is that it enables people to waste other people’s time.