For me the convenience of “hey remember this fact” is outweighed by a desire not to get stuck in a search or context bubble.

It might be nice to have better UI to control which bits of history get added to the context of a chat, but then just use a coding harness instead of web UI

Maybe. But I don't just use it for coding. For instance one thing I use it for is helping me track and evolve my workouts over time. It helps that it can remember the weight and number of reps I did the previous time. I could make an app for this, but it works well to do it purely within chat, with memory, and that's convenient. This is just an example, I use it this way for a number of things. I'm not going to use a coding harness for this kind of trivial use case!