It doesn't matter if the AR wasn't in Halo 2, they were experimenting with dual wielding, a brand new mechanic to the halo games. Who would pick up an AR when you can hold TWO GUNS!
Of course they realized their mistake cause people in halo 2 weren't throwing grenades or meleeing and returned the AR.
The only reason that people would choose the BR over the AR a majority of the time is cause its more efficient. That doesn't make it the signature weapon.
A spartan laser is the most efficient weapon IMO, its a one hit kill and its fast, not to mention I can probably beat Campaign on Mythic if I had one with infinite ammo.