No way I'd advocate something like that for every attack. That's why the extra rolls would be only when someone got hit with a critical.
If you think about it, that covers a lot of damage for relatively little extra complication. Who wants to roll every time to turn the goblins 3.5 average damage into maybe 2.7 average damager (or whatever the math works out to be)? Getting dinged down a few points at a time is the point of having AC and hit points in the first place.
Criticals are already sitting a bit uncomfortably outside of normal AC and hit point methods anyway. We have them, because people like them. So a bit of back and forth isn't so bad on those. And whereas I don't much care for a "confirmation" roll by the guy doing the crit, the idea does appeal of, "Hey, the orc critted you, max damage," goes kind of well with, "Hey, I rolled and blocked him with my shield, I only take normal damage instead."