I still don't see how it would make the combat any more realistic.
You still have no real idea how much that critical hit for 12 damage did. In fact sometimes it's even better to know how much you did. It gives you a better feel of how strong the thing you are fighting is.
For example, if you roll 20 damage at level 3, and the DM says "The creature bareley flinches, and lets off a gutteral laugh as he swings his wickedly curved blade down. *roll roll*", you know you might have a challenge on your hands. And by the same token you still really don't know how much relative damage you have done. Perhaps the creature has 40 HP and a high pain tollerance, or perhaps the creature has 300 hit points and is just there to make you run away.
DnD combat is not, has never been, nor will ever be "realistic". The very concept of the amount of punishment people can take, the abstract way armour and stats effect damage and to-hit rolls at times, etc. It's designed to be a simplistic combat system, not a realistic one. If you want a realistic combat, try Shadowrun. There a bullet can kill. Even a very tough character can be taken out of action (At least for a while) with one bullet. A dozen modifiers effect combat at any one time... range, light level, environmental conditions, your health, what type of recoil suppression you have on your gun, etc.
Of course, I hope you can do lots of math in your head quickly, or have a calculator... and a small vat of D6s...