Eddas story became part of PotD story because PotD and Nybeth made it possible for her to be that way. I mean HoH itself also barely had a story because most of it was about something that happened outside of it and thus the need for HoH was created. Do we know why it was created that way? Do we know how old it is? Do we know how the monster came in there and why we have our god animals in there too? Do we know why each boss exist? For me HoH and PotD are quite similar to each other. They are both a place were the story stuff happens.
I mean if we take it that way to we truly have much story in FF14? For me the places are more there to create lore (which both do) and to have a story happen in them. They are foundations that are needed to make the story work but not necessarily are the story. I mean for example any city state is not a story itself, but are the place were different stories happen while we still learn more about the place itself as lore.
Because what exactly would have been a PotD story? Any person that created the PotD (like Nybeth) was an outside source and not the place itself. What story (and not lore) can you tell about a place?
Also a lot of the things you are counting for the story of HoH are not about HoH itself. The group exists without it and have other responsibilities too, Sarinas rebellion was also not really in touch with the tower, which was built more with the thought that something bad could happen somewhere in the future. Heck we dont even know when this has happened and when it was built. The confederate are also not completely linked to the HoH and just use it to get a new leader but their own story exist outside of that. So even here you have people that are only linked to this, exactly how Edda and Nybeth were linked to it.
In the end again its all subjective. You can argue and say that a good story needs certain points but in the end enjoyment of it, is still subjective. And I will keep it that way to not further go off topic.
Bosses: The problem is that boss 90 of PotD was still in the casual part. We are talking about bosses that are mostly in the hardcore parts and feel weaker than the 30 boss.