Accuracy, consistency and efficiency is the goal of action shooting.
Speed just becomes a result of efficiency.
Efficient shooting and efficient training.
The way to tell that that you are taking enough time for accuracy is seeing an acceptable sight picture and calling the shot.
Steve Anderson calls it “Shooting at the Speed of Sight”.
Dry-fire increases the speed at which you get the acceptable sight picture. Accuracy in live fire comes from group shooting. In the action shooting sports there are multiple targets at multiple distances. So, both dry-fire and live fire needs to incorporate different distances and multiple targets.
Stage approach is a different story but the accuracy and consistency is still relevant. The stage approach should allow accurate and consistent performance in the most efficient manner.