Except that this scenario automatically assumes that armor is pierced by brute force. Bypassing armor with a small but specialized weapon can't be portrayed with DR (Example, a guy with a dagger is a lot more dangerous to a full plate wearer than someone with a sword)
And for the realism, when you manage to penetrate armor one way or another, the one inside the armor typically takes the full damage or at least close to it (killing him most of the time) instead of just getting scratched as his armor absorbs the damage.
Armor is all or nothing. AC represents that, DR doesn't.
First off, armor is not always all or nothing. Warhammers were designed to damage through full plate via blunt force trauma, not by poking through a gap. If we wanted "realism", piercing weapons would have a significant miss chance vs Plate, bludgeon would have a high DR, and slashing would be neigh ineffective. And arrows were capable of punching through plate, but given the loss of kinetic energy from doing so, DR would be a reasonable way to model that.
But DnD is not realistic to that level. There's no actual "realism" difference between Armor as miss chance, and Armor as DR, because what a "hit" means and what "HP" mean are incredibly abstract, anyway. DR vs. a dagger could mean that the plate armor made it easier to deflect the blow, but that it was still tiring to do so, but less so than the dramatic dodge that would have been needed without armor.
The question, then, is what makes for a better game. And overall, I like the idea of almost all attacks doing at least something.