A lot of where I've benefited is in some marketing language. Rarely, or almost never has ChatGPT come up with something and I've thought "that's exactly what we wanted", but through iterations, it's taken me down paths I might not have found myself.

Unfortunately, ChatGPT doesn't have a good search interface, so I can't search through older chats, but I know when I was looking at re-naming our company, it didn't come up with our new name, but it lead me down a path which did lead to our name.

I was trying to understand a patent, and we were looking at the algorithm which was being used. ChatGPT misunderstood how the algorithm worked, but pointed to it's knowledge of a similar algorithm which worked differently, but was better suited to our purposes.

Calling this "free-association" may be taking some liberty. Many people would consider these errors, or hallucinations, but in some ways, they do look very similar to what many would call free-association IMO.

Long, long time ago (1999, before LLM's) I made a virtual museum exhibit creator for education. The collection explorer created a connected graph where the nodes were the works of art and the edges were based on commonalities from their textual descriptions. It used very rudimentary language technology so it 'suffered' from things like homographs. Rather than being seen as a problem, the users liked the serendipity it brought for ideation.

I assume free but not random association could be a comparable support for ideation in research.

Assume free-associations = hallucinations. Assume hallucinations are exactly what makes LLMs useful and your question can be rephrased as "Can you list some examples where LLMs were useful to you?"