I love the Tavern! But yes, there are some features that can be developed to enhance the game play. This is V.1.0 so be patient.
My idea is this: if your own Tavern is fully seated, you get the same "collection ready" notification on the left side to let you know. If this is blatant and in player's faces, they will be more likely to remember to look around to see what they haven't collected, notice the Tavern, and collect their booty. Right now, I suspect, people tend to forget the Tavern exists, and to check it frequently.