To be fair it can make more sense in a story heavy game, especially if the combat feels like it’s largely there to pad out game time.
In something like Dragon Age while I can handle the higher difficulties I find I’m just not having a good time on them, so I turn it down and play primarily for the story, characters, lore, and standard BioWare romance gallery.
Which even with the game being easy, I still having fun with it. More than I would on a higher difficulty, and it’s different from a book or movie in that it’s still interactive.
Though as somebody already noted while raids have plenty of lore surrounding them, there isn’t really much in the way of story actually inside the raid instances themselves.
So adding a LFR difficulty level with no loot just “for the story” is a bit of a moot point. There isn’t any story to experience inside the raid instances.