Our patrons are having these same issues. One list of checked out items from all the libraries is best for patron usability. Plus, I have noticed on my own account that once you return all of the books to a consortial library, the library's name is still listed when viewing your loans. You have to change "All Institutions" at the top of the list to "Has Activity." But, it defaults back to "All Institutions" the next time you login to your account. This is only going to add to the confusion for patrons - to have libraries that they no longer have books checked out from still automatically displaying in the list.
Our patrons are having these same issues. One list of checked out items from all the libraries is best for patron usability. Plus, I have noticed on my own account that once you return all of the books to a consortial library, the library's name is still listed when viewing your loans. You have to change "All Institutions" at the top of the list to "Has Activity." But, it defaults back to "All Institutions" the next time you login to your account. This is only going to add to the confusion for patrons - to have libraries that they no longer have books checked out from still automatically displaying in the list.