Back in Vanilla, I definitely remember a story leading into WC and VC. I didn't quest much to get to it, but there was lore about ST. I found out about that lore because I was researching why the heck there were elite dragonkin all around that place. But most of the places may have had their own story, but they didn't fit in to the overall world and story the way Dungeons have since Wrath. A few examples:
Wrath - the epic adventure through Howling Fjord, only to have Lich King snatch away the final boss and send him to Utgarde Pinnacle. Then at 80 you came back to UP and finally closed out that story line. Or going through the Coldara quests and seeing Keristraza sacrifice herself for you, leading you to go into the dungeon and "free" her.
Cata - All of Vash'jir culinates in a 5man (TotT) that was supposed to also include a raid that got scrapped. Uldum is practically a feature length movie (and spoof on Indiana Jones) leading up to Halls of Origination.
Mists - Temple of the Jade serpent is the culmination of Jade Forrest zone. Kun'Lai summit has a lengthy quest chain, whose story ends at the door of an instance. I do think the Mogu weren't introduced as well as they should have been, so Mogu'shan Palace felt like some weird, somewhat random adventure....
As for Stormstout Brewry, that's a huge step in Chen Stormstout's journey. The point is his family's legacy is being trampled and their brewry has been run into the ground to the point there ARE crazy hozen partying around and Virmen have taken over a part of the place as well.
To counter your point, you spent several hours not even running all of BRD. How can you say you even accomplished anything in those multiple hours when you couldn't even get to the other part of the dungeon?
I'll concede dungeons today are not as "epic" in length, but that's largely because they're being used as a piece of a larger story, like in Chen Stormstout's case. That's just one part of Chen's overall story line. BRD was, well, kind of integrated into the story. Parts of it were, anyways. Mostly it was just a place that existed and had some people in it and you went in and killed stuff for hours on end.