There are some zones where I have collected everything. It'd be nice if there were a preference where an empty minilist would auto-close / not-show, possibly as a sub-preference of "auto minilist".

Just a passing thought, thanks!

We tend to leave the visibility of the Mini List to explicit user control. Should lag cause a mini list to not see its data and then automatically hide itself, the mini list would erroneously be hidden and unable to process its data without being visible, thus being hidden until the user brought it back. As such, this request is too prone to error to implement into ATT.