Yea, I agree, that would be nice. There are ways to do this without it, but it's not ideal:
If you enable Areo you can use software window capture on the pop out chat window and select the sub-region where the chat text is, it works; you can move it anywhere (in some corner, over the edge, barely visible, if you don't want to chat), but it must not be minimized.
Alternatively, if you must have Areo disabled, you can still do this, but no other window must be over this one and it must be visible (can't move it over the edge because it won't capture that part), can't minimize as well.