Gotta give it to the demons, any plan that starts with "we're gonna fuck up the Moon" is an ambitious plan, if nothing else.
Ok, so that's 2/6 demon king pieces Ryu has destroyed. Considering this deal has been going on for almost as long as recorded history, you would REALLY think people would be more excited about that. Like "she should be treated like a god or at least a saint at this point" excitement. This is basically equivalent to someone coming along and punching up a second slate of Commandments except even MORE impressive because she's ridding them of a deadly threat that's been hanging around them forever.
Also, Ryuu HAS to explore this whole "guiding tree" thing at some point. Like seriously, even if you only ever intend to punch shit (and now chop shit up with your sword) at least see if you can't do it more efficiently or without needing to be healed for three days afterwards.