Don’t take this as me saying I do not install double leg movements in training. Bilateral movements such as the barbell back squat can be used to produce greater forces. This may lead to greater strength gains. There are a few training goals that bilateral movements do not address.
We can use single leg movements to highlight existing asymmetries our athletes may have. It can be difficult to spot an athlete favoring one leg with the naked eye. When having them do a single leg squat, we quickly see which one has more difficulty with the movement. We can also use single leg movements in training to combat asymmetries.
Most movement in sport occurs on only one leg. An athlete needs to be able to stabilize our body on one leg, whether it is static or dynamic. Single leg variations can help an athlete apply force with balance and stability.
There are a few things to keep in mind when using single leg movements. Some movements, such as a lunge use the second leg as a support leg. This reduces the amount of instability and allows for greater force production. When doing a pistol squat, there is no extra support. This increases instability and decreases the amount of force that can be produced. Single leg movements can also be performed in multiple planes.
This is seen in a lunge, which can be reverse, forward, lateral, diagonal, or an angle between. Single leg movements can also be performed in a continuous or alternating fashion. Alternating legs requires the athlete to reset between each rep. It also allows for a slight recovery of the prim movers. Continual reps on one leg allow the athlete to get into a rhythm but does not allow for recovery between reps.
There are many other reasons to install single-leg work into a program. There are many more variables to consider regarding the level of athlete and the goal of the program. This is just the basis for my rationale and the first variables I think of.