Deal with this stuff when we are creating living shorelines/wetland creations. Is a pain to eradicate, once establshed its a constant battle to get rid of it. I tell customers when we build wetlands to keep an eye out for phragmite to keep it from getting a foothold in the wetland.
It is unbelievably aggressive plant. It takes multiple sprayings to kill to the point where it can be kept under control and burning it just gets you a leg up on it. Leave the area alone and it will reestablish itself in short order.