The first-person camera is a subjective camera angle. Developers that use this camera, use it intentionally to embody you into your on-screen character. It is used to make you feel like you are the character you are playing, to experience a first-person role of immersion.
GTA however, has always been about the character you are playing, and therefore wouldn't work in a first person context. They don't want you to be the player, they want you to experience what the character is experiencing from over his shoulder.
Also, switching from third to first, and back and fourth brakes immersion, and doesn't allow the game to be fully appreciated imo.