Balance drills are supposed to help stimulate the proprioceptors. Specialized structures found in joints, muscles and tendons. These small organs are the peripheral termination of sensory nerves and provide feedback to our brains regarding body and limb positioning in space. Besides joints they are especial plentiful in the soles of feet, palms of hands and the genitals. Physical therapists use balance exercises a lot particularly to help people with recent joint surgery or major limb damage. They can also help stoke patients who's injury is in the brain and not peripherally, by increasing the sensory input to the brain and thus compensating for the central damage. These exercises are apart from strengthening the muscles, altho the exercises also do that to some extent. Its been found that even in normal, undamaged limbs this proprioceptive stimulation can heighten one's ability to use their limbs athletically. I believe the guy that wrote "Steady Ski" has a physical therapy background.
As a person who has had both knee ACL's repaired plus other, extensive surgery on one of my knees, I can say its helpful for me. As a physician I know that these organs do exist anatomically having learned about them in anatomy class. Its not pseudo science. The problem is that they have to be practiced faithfully and regularly to see progress. And they are somewhat BORING! I'd much rather be skiing. But, like working out in a gym, its one of the things you can do to ski faster, particularly for us older skiers. Maybe they help injured athletes more than young healthy ones. I don't know. If you believe the guy who wrote "Steady Ski" they're a panacea for everyone.