TL;DR: Use the main locking knob to lock the head when taking a picture; the friction control knob is set once (and then left alone) to prevent the camera from flopping over when you unlock the main knob.
When you unlock the main locking knob on a simple ballhead without a friction drag knob, the ball and plate are free to move. If you aren’t holding your camera carefully, that means the camera and lens are free to move as well. They could easy flop down, hitting the stops or limits of the ball’s motion. This might not be fatal or catastrophic for your camera, lens, or attachments to the camera, but it’s never a good thing.
But with a friction knob on the ballhead dialed in to the right setting for the weight of your camera and lens, when you unlock the main locking knob, there is still some small gripping force on the ball. It requires just a light but deliberate force to move the camera’s position. If the friction is set just right, you can move the camera to any desired position, let go of the camera, and it won’t shift, even without locking down the main knob. Of course, you should lock the position tight by tightening the main knob.
I said “if the friction is set just right” because in my experience, a very small change in the position of the friction knob means that either it’s too tight (I can’t move my camera without lots of force, meaning I have no control for fine positioning), or it’s too lose, meaning the friction is not enough to stop my camera from flopping over when the main knob is unlocked.
If I were to use the same ballhead with the same camera and lens combination all the time, then I would dial in the friction once and rarely think about it. However, because I use different cameras with different lenses on my ballhead, I have to constantly find the just the right amount of friction for each combination. This slows me down, to the point that I never use the friction knob.
Furthermore, the amount of friction required to keep a ball from freely moving depends on the position of the ball. For a ballhead with the combined camera and lens center of mass sitting directly above the center of the ball (i.e., the mass on top of the ball can be modeled as an inverted pendulum in static unstable equilibrium), the friction on the ball required to keep everything in position is minimal.
However, if the mass of the camera and lens combination were far forward, then a large torque is imparted on the ball, requiring a lot more friction to keep the ball and camera from moving. The Arca Swiss Z1 ballhead attempts to counter this by having an aspherical ball (think egg-shaped, but not nearly so pronounced; it’s not visibly noticeable). When the ball on the Z1 is rotated out of its vertical position, its diameter relative to the width of the ballhead’s body increases, thus increasing its own friction as it rotates away from top-dead-center, without any additional mechanical complexity.