Because it's more simple.
Player's avatar arms are one thing to tweak and make look right in a 3d world. If you add the full body, it takes more resource to accomplish, and does not always add much to the gameplay.
If you use only the arms, you can have the arms and the gun in the frame of the camera; while if you use a 3d body as well, you'll have to tie it to the world frame. You then have to take a lot of things into consideration: what if there is an explosion and the player's avatar gets launched in the air? Would the motion of the camera AND the motion of the body of the avatar match and be adequate in their look and feel?
Also, consider mouselook. If you use only the arms, you'll have less limitations that if you use the full body. If using full body, the designer might want to restrict the player from being able to target their own feet ("Dude! I'm shooting my own feet and I'm not even losing health!!"). Simply making an animation that looks and feel right when the player looks all around is, again, more expensive than just using the arms.