You've added language that does not exist in the rules and the rules clearly state that dice are resolved one at a time (unless combining with a modified value dice.)
What does resolving them one at a time mean? It means you fully resolve the effects of one die before moving to the next, rather than as one big simultaneous action. It means that multiple damage results can be distributed, and each counts as a unique instance of damage, etc.
It doesn't really say anything about whether you go back to the pool to pick a new die each time.
Again, I don't have to add language. The rules state:
A player can only resolve dice in their own pool. A player can resolve dice with different values during the same action, provided the dice share a symbol. (RRG, 14)
The Dice Pool is defined: This is where dice are rolled. Each player has their own dice pool. Dice are always placed on their matching cards when not in a dice pool. Dice in a player's dice pool can be manipulated (removed, turned, etc.) or used as a reference for card effects that require a specific side to be showing. (RRG, 10)