Phragmites is also used in Traditional Chinese Medicine to clear fevers, coughing and congestion, and help with stomach issues such as vomiting. The stems are used in this case. I've used them myself and they are a mild, but effective herb.
FYI the type used in TCM is Phramites communis or common water reed, which sounds similar to australis.
From the book of Native American Ethnobotany Phragmites australis was used to treat diarrhea, and the sugary sap was used in pneumonia to loosen phlegm and soothe lung pain. The stems were dried and beaten with sticks to remove the sugar crystals, seeds were used for food, and the sap collected and used like candy. It was also extensively used as fiber, splints for broken bones, making arrows, and a lot of other functions.
Very interesting plant.