I think we know what the real badass boss speech was "Don't flatter yourself." Azula (It's both a bad ass boss speech and a peek into the tragic expectations that have been forced on Azula even by herself)
The fire nation hat/crown thing could be because they're fire lords? Like maybe they used to just make the avatar fire lord until like at one point before Roku was born? Like maybe Roku was the first avatar from the fire nation to not also be Fire Lord?