I think Annie doesn't get very much love because her personality is kinda one note. Like, there's nothing wrong at all with being cute and little and innocent and silly and seemingly weak. It can be very charming! But throughout the game, that's the majority of the view we get of her from Caribdis. We aren't given other interesting winkles, for example maybe she struggles with some addiction, or maybe she experienced some sudden loss that makes her very risk averse, or maybe she learned that love was conditional based on some certain criteria. Elements like these would give her some more depth.
As some previous posters noted, she does many critical things to keep the plot going. So she is absolutely important, she's just a little dull compared to many other characters.
