Lead or be led
Taekwondo students constantly train to execute any technique equally well from either side. However, most still have a good and bad side, they never achieve equality on both sides. Also, most have individual techniques that work better on one side than on the other. When right-handed fighters fight with a left-lead, they usually use their right arm and leg for attacks. When they fight from a right lead, they still use their right arm and leg for attacks. The reverse is also true for left-handed fighters.
So, with all the emphasis and training on learning to fight from both sides, why do Taekwondo students still fight from primarily only one side? Maybe it is because the single-lead is the best way to fight!
If you analyze the situation, the single-lead logically appears to be the best way to fight. If two fighters train the same number of hours with the same intensity, one using only a single-lead and the other using a double-lead, then the single-lead fighter will have trained twice as much on his one side as the other fighter will have trained on either of his sides.