The entire Star Wars saga wouldn't have happened without Jar Jar Binks. The Lord of the Rings wouldn't have happened without Celebrimbor. Remember him? Being a functionally important character doesn't make one an interesting character. :And yet the entire story wouldn't have happened had it not been for her.
My problem with Annie isn't really with Annie, but with how underused she is. Her initially most defining trait (being really into/knowledgeable about Eternum) loses its significance once the other characters start getting good at it, too. I wouldn't mind a story development that really reminded players of/drove home who the real Eternum wiz is.