No, this is not a thread about whether or not ZOS should add a story mode for group dungeons. I think group dungeons are okay as they are now.
I soloed Vaults of Madness on my PC NA main the other night. It turned out to be my first time running it on PC NA, so I did the quest and went slow. I'd already run the dungeon with guildies on PC EU, but we had rushed through, and I didn't remember the quest. Since then, I've soloed it twice on my PC EU main, but couldn't go through the quest again, so I enjoyed being able to go at my own pace and experience the story.
Today I soloed Banished Cells I. I'd done the quest before, but I don't think I'd carefully read through all of the documents associated with it. I wasn't able to repeat the quest as a quest, but I thought it was interesting that I could more or less repeat the quest by talking to the keeper and observing all of his conversations with all of his fellow keepers. That, in addition to leisurely reading all the documents left by Rilis, helped me to really absorb and enjoy the story.
In contrast, when I repeated Vaults of Madness on a character who'd already been rushed through the quest, I didn't have an opportunity to interact with the three quest characters at all until the very end, after I killed the Architect. The only way to experience the quest and enjoy the story was to do the dungeon on a different character who'd never done the quest before.
Are there any other dungeons that let you repeat the full stories of their quests by interacting with the characters again, the way Banished Cells I does?
I've fought mudcrabs more fearsome than me!