@LiquidFeet, this is a good summary. Pivot slips are what we ski instructors call a highlighted task, which is a task that highlights (not isolates, but highlights) a specific skill. In this case, the highlighted skill is rotation, but the task also requires edge control and fore/aft pressure control skills as well.Practical application? Oh my. With a little tweaking, pivot slips can morph into very short radius turns.
The active rotary of the skis/feet/legs in pivot slips without hip/upper body rotation comes in handy in all kinds of situations. The lack of upper body rotation keeps you stable, whereas the upper body will want to keep rotating if you allow it to turn with the skis so keeping it quiet is a major accomplishment. If your upper body keeps rotating even a little once your turn is done, you are done.
So these super short rotarized turns without upper body rotation are useful on hard snow that's steepish - when you want to ski in a narrow corridor without mach schnell speed. In other words, you can learn to make speed-controlling short turns down the fall line on groomed black diamonds that are skied off. They are also useful if you want to go slow in hard bumps (the ones I'm familiar with here in NE) straight down the fall line. You can actually ski a more-or-less direct line in bumps at a glacial pace, if you've got pivot slips in your tool box, then increase speed at will. If you like to travel along in the ribbon of soft shavings ("snow") at the side of the trail once the trail is skied off and want to slow that travel down, you can use super short turns there too.
I'm sure others will chime in with other reasons to get pivot slips in your repertoire. Backwards pivot slips? Not so useful, but fun anyway.
So, what are the practical applications of the skills learned doing pivot slips? These skills are really key in skiing terrain. In skiing terrain, you may find your line limited in bumps by a lack of snow, a presence of rocks or organic matter, or a nasty adjacent bump. Because of the time and effort you spent on learning how to link pivot slips, you might find it possible to ride and slip along the ridge of the bump, pivoting your skis to avoid the organic, mineral, or hydrologic features in the terrain.
Linked pivot slips teach you upper and lower body separation. Such separation is a key to skiing bumps or steeps, where the ability to steer your skis is paramount to picking a line that is dynamic, slow, controlled, safe, survivable, or aesthetic.
Pivot slips with retraction (as the skis rotate to be in the fall line, retract your legs and change the edge in a very compressed position, extending as you steer the skis from the fall line to a slide slip) helps you learn how to tip the skis to a new edge from a very compressed position. This is a key skill in skiing steeps and bumps. This is a drill that highlights the fifth fundamental -- the regulation of pressure created by the interface of the snow and the ski. Mastery of the fifth fundamental, in my opinion, is the magic glue that opens the door to expert skiing not only in terrain, but on the groomers and in the park as well.
So, don't dismiss pivot slips. It should be a drill that you practice often. Go for mastery, not just competence.
Mike