I'm curious from the other direction, what are the conversations like if you feel they are easy to move?
Do you have the memory feature disabled? I have the feeling this in particular is doing absolutely loads behind the scene, e.g summarising all conversations and adding additional hidden context to every request.
I can start a new chat in the UI right now, ask it what my job is, what my current project is, how many kids I have, what car I drive etc. It'll know the answer already.
I think it's this conversation history - or maybe better yet if we think of it as this "relationship" - that people are saying is going to make it hard to move.
I ask for code snippets, occasional recipes, translations... I don't have memory enabled. I start a new chat for each question. At times I ask things in different languages, if the question is tied to culture or location. If I notice I asked the wrong question, I start a new session instead of continuing the old one, so it doesn't try to merge the questions somehow.
I don't see any benefit in it knowing anything about me. Instead I'm usually quite vague to avoid biased answers.