The player doesn't bob. View bobbing is to make the view bob, because why would it be called view bobbing if it wasn't for the view? In case you didn't know, view = camera.
Tell me where it says "player" in view bobbing.
Oh my god, man, 60% of my gameplay is in 3rd person, i think i'd know.
Did you even
try to do this?!
Probably not, so, I'll just record it.
http://youtu.be/FOCfleHe8d0Jesus, I've been playing the game long enough, I think I'd know what I'm talking about.
So even though first person is from the head, your reasoning for the bobbing still doesn't make sense.
Neither does the fact that when in first person you always have view of your player's right arm, while in third person they are at your sides.