would propably make first person better for those people who don't know that they can adjust it/turn it off

imo the main reason head bob is so annoying, is because it does not feel right, the ay it is.
a healthy person (in matter of the sense of balance) will usually compensate it's head movements while running with the movement of the eyes, so that you keep looking at the same spot (if you can't (eg. in a ship in heavy sea) you may get (sea)sick)
so the only thing that would change is the height of your eyes
the way i currently experience head bob (don't realy do, as i have it turned off), is that it's like you were looking through a helmet camera (or with your eyes fixed in one direction), so the when the head tuns down by 10°, the camera will do the same
irl, if you head turns down by 10° you eyes will turn up by 10°, so you will still be looking at the same thing (just from a bit lower, as the center of your eyes moved down a bit(trigonometry ftw))

I agree with this 100%.

I have never used this in arma, and i have always advised people to turn it off; headbob has always felt forced and unrealistic to me.

Headbob seems to be trying to artificially recreate something that isn't really percievable in the real world as it is... (to me anyway, not when i'm sober.)

Let's call it how it is, if you turn on headbob, your character looks like he's drunk..

Finally, something you haven't touched on yet, (and this is why i imagine most people turn it off) headbob also makes it harder to identify things when you character is moving... Therefore if you leave it turned on, you are leaving yourself at a (however small) disadvantage in a competitive environment.