Lunges are hard. Step ups make people groan and roll their eyes.. and don't even get me started on things like the Bulgarian split squat...
I've seen, literally, guys who can squat and deadlift four to five hundred pounds but fall over when they try to do a lunge with 40lbs. That type of discrepancy is a big red flag that there are some lagging muscle groups.
Despite most people's feelings of utter loathing towards single-leg work, it's uber important to regularly perform such things for the following reasons:
Main points of the video:
1. Even out imbalances between sides (from head to toes, quite literally).
2. Challenge and strengthen the smaller stabilizers muscles of the foot, ankle, hip, and core. The bigger muscles often compensate for these guys so it's for them to get lazy.
3. Prepare you to perform normal human movement like, running, jumping, dashing side to side as your sprint down the field or racing your kids upstairs, you know, normal things.
Personally, I've stepped away from squatting and/or deadlifting for a couple weeks to work on single-leg work and when I came back to the bilateral movements, I felt much more solid and tighter- probably because I was able to strengthen my stabilizers and reduced any overcompensation that was happening on one side to make up for the other.
Now you don't have to drop squats or deadlifts, but putting a little more emphasis (or any emphasis at all) on your single-leg work will prove to be a useful, if not DOMS-inducing, addition to your training.