So new players crouch behind something thinking they're safe. Get their heads blown off from the front and can't work out why!
(spontaneous guess) To better align with the position of one's firearm. This allows the game to calculate projectiles as originating from the center of one's screen without too badly breaking the illusion of where the visual projectiles is originating, as the muzzle of one's firearm is nearby, and where it would be going if it actually originated from there. A while ago there was a thread (maybe two) analyzing the curious flight path of Lightning shells due to the discrepancy between where the visual projectile originates and where the functional projectile originates. As a possible aesthetic bonus, you see a lot more of the firearm model without looking like it's being held in an odd manner.
It's necessary to have this in all FPS games. The view just doesn't "feel" realistic if you actually do it realistically. The Devs from Mirror's Edge discussed this at length in some interview I can't find anymore . That's a parkour game where it's necessary to show your hands in the view. Things in Mirrors Edge as well as regular "shooters" get downright off if you try to put the camera centered in the head of the player. They have to do a fake view to give the illusion of a real one.
Bullets are shot from the center of the screen. If the center of the screen aligned with the top of the head then bullets would shoot out of people's eyes. It would 1. look really odd 2. mean that people could sit down behind complete cover with nothing showing and shoot people at any angle. It's conventional to show the gun people are holding on the screen instead of having a separate entity in the world for the gun. A realistic camera looks unusual in games because you hardly ever see it.
It might also be boring because if a gun is held at the hip it will be outside your field of view when looking forward. I don't think people would want to run around in ADS mode all the time. Blocking your view. Same goes for melee weapons. In real life your weapon will be outside your field of view most of the time. It's only when it hits target that you will see it for a second or half. Games tends to show the hand holding the sword. In real life a sword held at the hip will only reveal a mid section of the blade. A sword ready for a quick strike will show a bit of the tip and a sword ready for a big swing will be outside your FOV.
You can get immersion mods for skyrim that make the first person camera just a camera from the eyes of the character using the regular world animations. Fighting with a sword really does just show flashes of the tip of the blade. You see this sort of thing in games that were designed to be third person games but have an added option to flip to first that didn't get much priority.
