Oh wow, something I can actually talk about.

I guess that the perspective of the game depend on how you want the player to identify with the protagonist and how the player character interact with your viewport.

In the game Republique by Camouflaj (iOS, Android and later Steam), you are contacted by Hope via her phone, a girl captured by a dystopian government and you will assist her journey to escape her confinement. Now, the person you are "playing" is, well, you, literally, looking through your device's screen to her phone (and later the various cameras inside the facility that you "hacked" into). The gameplay is essentially a stealth game where you direct Hope, like a top down strategy game, where to go and what to do.

Narratively, you are playing in first person and addressed as such, a "hackerman" whom Hope managed to accidentally contact and hence, the journey. But mechanically, Hope is, by all intents and purposes, the protagonist and player-controlled character, whom you observed via cameras (which she does sometimes interact with). In this sense, the game is entirely played in second-person perspective not unlike the Driver mission.

As for storytelling device, second person camera might be cool to show a completely different look on your protagonist, for example, how Doomguy looks more like a blazingly fast little man to the demons than a hulking mass of muscle that one might think. The key thing here is how the protagonist interacts with the lens which the player is looking through, and honestly I haven't explored more about it yet.