(1) disguise as an LLM to have them give better problem descriptions to you (2) provide an LLM for your users that lets you read their chat to understand their problem

and:

(3) try to understand why they are communicating differently to an LLM. Immediate replies? Different feelings knowing they don't talk to a human? Genuinely better help? Not getting treated as stupid?

All or none of these may be true, but if it's consistent behaviour then there is a reason for it.