Wouldn't it heavily promote (particularly for zergs) upgrading speed (and possibly agility) instead of armor, to increase a unit's expectancy ? Or making a unit with enough armor to only take 1 damage from attacks virtually invincible if it's not extremely outclassed in terms of speed.
I'm not criticizing the choice of regeneration here, only questioning about the implications of the "on every attack attempt" thing.

Eh, I think it is just fine the way it currently is. Such an idea might be necessary later, for balancing issues, but not under the current circumstances.