"The Pit and the Pendulum" is one of those stories that had to be written in the first person. If we weren't hearing the tale right from the source, it'd probably be a total bore. Nobody wants to hear "And then the blade swung closer and our hero looked really, really scared." No, we want a deeper, more visceral experience – one filled with all the memories and sensory experiences that only a first-hand account could contain.
Now, it's important to note that "The Pit and the Pendulum" is told in retrospect; our hero, having survived his ordeal, is now writing it down. This is key, really: if he were in the moment, the entire narration might sound something like this: "Holy crap, oh shoot, oh man… what the heck is that swinging thing…gah, these rats are gross!" So yeah, good call, Poe.