Iirc, Kurandara did appear alongside other battles, and battles did refresh/vanish – although it was a little bit bugged as well, because I don’t think the dev team expected people to consistently skip Kurandara (i.e. after a time, he was the only option, but this wasn’t the norm):
Screenshot or image:
Okay, now that I defeated Kurandara, the map reset:
In this case, though, the points from AW do scale, even though he may appear less frequently than the 1-2 battles that an efficient player will focus on, so the break point for the number of Sigils you’d expect to use before it becomes profitable to skip AW is probably a bit higher than for the Kurandara event.