This isn't exactly an answer to the OP's initial question, but I would like to point out one or two examples of smart game design using the game's 1st or 3rd person perspective. I think Metroid Prime made interesting use of its 1st person viewpoint with the information from the visor. As you could guess, the player sees what Samus sees from inside her Power Suit through her visor. This is interesting because for one thing, it fluidly integrated the UI of the game into its world. But it also allowed for immersive visor effects (a jet of steam visibly clouds up the screen; a flash of light occurs and you see Samus' eyes in the visor's reflection). The first person view could have been just a new viewpoint for the Metroid games, but the developers decided to make it more than that. The 1st person perspective in Metroid Prime is a tool for immersion, environment building, and it fleshed out Samus' iconic Power Suit.
Also, the integrated UI that I mentioned can also be found in another form in Dead Space, a third person game. In Dead Space, the information the player needs (health, ammo) is not displayed in a generic HUB, but is instead shown in the world of the game. The health bar is on the back of Isaac's suit, ammo count appears as a hologram above a weapon when you aim it, and all other typical menu info appears as a hologram displayed in front of Isaac in real time. (Isaac's head even tilts to look at the different menu info as you scroll through it on the hologram, which is one of my favorite details.) This is how Dead Space achieves a similar feat to Metroid Prime in clever game design using the game's perspective.
By the way, I usually prefer a 3rd person perspective.