I had to go and check out a YouTube walkthrough again to come to this conclusion but I do not believe you are sent to Peryite's Pits in Oblivion despite what some wiki articles say. And yes, even though on the map screen is says "Realm of Peryite", I believe this is in error and was overlooked.

For one, listen to what Peryite says carefully.

He says their souls are in Oblivion and that he will "transport you to the plane of Oblivion in which they are trapped." Not once does he refer to his own realm and by his message, it's clear it is another realm other than his.

Also, Daedric Princes are nigh omnipotent in their plane. Knowing that the souls were there, I'm sure he could have rectified the situation himself. It also begs to ask why his own minions would attack you or the souls trapped.

The last one here might not be too compelling, but I would imagine Peryite's Pits would look like an ever descending series of.... pits or craggy mountains with bottomless chasms. Instead, his realm looks exactly like Dagon's with nothing to suggest any kind of abyss or holes.

In conclusion, what we see in Oblivion is definitely not Peryite's Pits. Instead, it's probably the Deadlands or a demi-plane in Oblivion. So, will we ever see The Pits? Seeing as how it is considered the most inaccessible realm, not anytime soon perhaps.

Most likely the character was going to visit the Pits but the devs decided that they only wanted to make one plane of Oblivion so we went to some other realm. Also it has been mentioned that no one has ever been to Peryite's realm.

Budget and other design issues. It'd take up too much time and money to create brand new models, textures, and a whole new enviorment just to use during one non-main quest line.