I'd also point out that this could easily open up a new area of narration that binary hit/miss can't - wearing the opponent down to the point where it cannot continue.
Imagine for a second that the fighter with GWF is facing 3 hp kobolds. Now, he auto kills one kobold every round, whether he hits or not. But, how can we differentiate the narration? If he hits, he splats the kobold, fine and dandy, no worries. If he misses though, maybe the kobold screams, drops his weapon and runs away. Maybe the kobold cowers on the ground, too scared to keep fighting against this engine of destruction wading through their midst.
IOW, we can narrate a death from this as a morale failure, rather than a straight up death. Since HP loss isn't necessarily actual physical damage, this opens an entirely new area of narration that can lead to all sorts of interesting RP opportunities (after all, if you simply kill all the kobolds, there's not a whole lot of RP going on afterwards).