The narrator of "The Murders in the Rue Morgue" is upfront about his own personal tastes, and when we say upfront, we mean it literally. He spends the first several paragraphs of his story expressing his admiration for certain kinds of thinking, which he finds in his pal Dupin. We sit back and watch him express his awe at the man's genius the first few times and we think that he's justifying why he has selected Dupin as the protagonist of his story. Fair enough. And when he spends whole pages on one chain of reasoning from a fruit-seller to Chantilly the actor, we think, well, maybe this is getting a bit heavy with the hero worship, but we can deal. But as the story goes on and the narrator meets every new thing Dupin says with "mute astonishment" or "this is beyond my comprehension," we start to wonder why expressions of amazement are so important to this story.
There are a couple of things that this "awe" might be doing. First, the narrator's astonishment gives a plot-level reason for why Dupin needs to talk through his solutions carefully and slowly. Second, it signals to we, the readers, that we're supposed to be similarly in awe of what Dupin is doing. And third, it increases the suspense. The gap between the narrator's understanding and Dupin's keeps us on edge, as we wonder what Dupin knows that the narrator does not know.
The narrator's constant praise of Dupin's uncommon genius reminds the reader to imitate his methods of thinking to solve the puzzle of the story.
The narrator's awe-struck responses to Dupin slow down the dénouement and step up the suspense of the narrative.