School figures as they existed in standard ISU competition from the 1890s until 1990 were pretty simple (1 or 2 turns per circle, or the rockers and counters happened at the change from one circle to another with just a continuous edge along the whole exit circle) but they were not especially brief because each whole pattern was skated 3 times on each foot.
Also everybody did the same patterns. So there was no need to communicate a layout.
Or are you thinking of
"special figures" or "
fancy figures," where skaters made up their own patterns and submitted them before skating them?
That was part of the sport at its beginnings in the 19th century and in the early years of the 20th century, competed at the 1908 Olympics:
And also this kind of thing is now promoted by an organization called the
World Figure Sport at their
World Figure & Fancy Skating Championships.
There skaters made/make up their own complex patterns, often symmetrical and therefore repetitions compared to the combinations of edge skills shown in the program videos I linked earlier.
Certainly someone could include those kinds of skills as transitions or within a choreo sequence or step sequence in today's programs.
If you want to see the kind of skills involved, just watch the one-foot clusters in today's singles' step sequences aiming for level 4, or the one-foot turns sequence in today's free dances. Although those also include twizzles, which were not part of either standard school figures or special/fancy figures.
However, the main point of both versions of figures was the pattern drawn on the ice, which required
clean ice without other markings so that the tracings would be very visible -- the recent competitions in Lake Placid use black ice, which makes the tracings even more visible.
This would never be true in today's freeskating programs, because each skater uses the whole ice surface for their programs, and for their warmups, so even by the time the first skater starts their program there wouldn't be significant areas of clean ice and by the time the 12th skater after the last resurface starts their program, after two warmups and 11 previous skaters, the ice would be very marked up already. The tracings that the current skater just made would not be easy or often possible to distinguish from all the other markings already on the ice.
And there's no way that the whole surface would be resurfaced between every skater.
With school figures competition, skaters only used a small patch of ice, and the next skater would use another patch further down the ice.
Resurfaces were sometimes done on part of the ice at a time with manual equipment.
But it was all a time-consuming process, which made that an expensive part of the competition to run, especially since it wasn't a part that audiences were interested in buying tickets for or TV networks in spending much if any time to broadcast.
Including brief sections of figure-like skills in free programs would not add significant time and would not require clean ice. But they wouldn't showcase the patterns drawn on the ice the same way that figures competitions (or programs like John Curry's linked above), executed on clean ice, did.