I wrote few years ago about the same subject at this article, Fall Prevention Programs; are we provocative in the right direction?
Nothing seems to change and this bad practice and misunderstood approach to increasing balance is still the norm.
Instead of reducing the base of support, for example from wide stance to a single leg stance, one need to focus on how he stands.
Learning to balancing and moving from the hip is what needed, not standing on one foot per se.
Could be nice to do a research about people going through a fall prevention exercise program with standard drills like the video above, with the single leg stance, and compare with drills in which the focus is movement from the hips.
Somebody wants to go ahead with this type of research?