I love this article from Nobuo Sato about his love for skating skills and compulsory figures. He mentioned about John Curry and Lori Nichol too.
Nobuo Sato with 50 years of coaching experience talks about "The awesome skills which was handed down to Mao Asada"
(My rough translation)
1990 was the last year when competitions had compulsory figures. After eliminating compulsory figures from competitions, medal contenders for 1991 Worlds changed drastically. It pushed skaters who can do jumps up to the top contenders. And it made a 180-degree-change happen in the history of figure skating. Taking it into considerations, maybe it is no exaggerations to say figure skating of the days when compulsory figures remained strong and the current figure skating are totally different sports.
That said, I think it's safe to say compulsory figures are one of the essential training for improving in "skating" skills.
Can you draw a circle and come back to the exact place where you started? How do you make it? Skating needs the skills you used here. While compulsory figures disappeared from current competitions, it won't be changed permanently that knowing school figures is helpful for you.
It's not serious compulsory figures where skaters drew circles in old days but it's more like introducing "compulsory figures" by requiring skaters to do complicated steps and tell "Learn this and that edge works and turns." This is today's free skating.
Actually there are coaches who acquired good skills in compulsory figures. They surely teach compulsory figures to their students even if not much. In Japan there still remain compulsory figures in "badge test" (a qualification test from level 1 to 8 which are required for participating in competitions) where skaters are required to draw a semi-circle (skating on one foot and drawing a half circle) and do change-edges and various turns within the semi-circle.
I sometimes feel skaters who acquired good skills in compulsory figures are pushing up the level of skating. Using accurate edges gives a birth to a clean arc. I don't mean the beauty appears in a trace but I mean the beauty appears in the movements. Such movements are very accurate and very beautiful. Those beautiful movements with no useless power should be remained, I believe.
That being said, while I keep my thoughts in my mind, if I'm asked "How much will it be reflected in scores under current rules?", my answer will be "almost zero." No matter who says what, skaters who do jumps will win. Then the story goes like "Don't waste your time for working on compulsory figures and try one more jump instead."
In current competitions difficult jumps and excellent jumps are shown one after another and it became the main stream of deciding who wins. This phenomenon is the result of eliminating compulsory figures from competitions and at the same time it is one of the reasons why figure skating drew world wide popularity. So it can't be helped.
That said, the essence of figure skating will never be changed. I believe we should not leave skating skills forgotten. How wonderful it will be if a skater does cluster turns with accurate and beautiful edge works! I'll be thrilled. I have strong feelings in my mind that I want to hand down the skills such as "You need to use your upper body in this way for doing accurate and beautiful edge works" to next generation or the one after the next.
To me skating is something smooth to the end of the world. It's smooth and fluid, and never be forcible with useless power, it should be smooooooth, just like being pulled by someone under the ice. This is my ideal. I keep my ideal in my mind and talk to everyone around me "Let's challenge it!"
When a skater looks like just simply "skating", s/he is using skills. Put your weight on your left foot, for example. If you stretch your left knee, of course your center of gravity goes up. The slight stretch of your knee will naturally make you glide forward smoothly. On the moment you may have an intention to push the ice. Or you may just keep your knee stretched to prepare for a next movement. Such difference makes a surprisingly huge gap of speed in 5, 10 or 15 strokes. Even when a skater looks like just simply skating, skills are needed for skating.
Seeing someone skates with feeling the difference of every stroke one by one makes me thrilled and I can't help but saying "What a wonderful skater!" to myself. Among current top skaters Carolina Kostner is one of the skaters I feel attracted to. She's such a skillful skater.
Also I felt "Wow How skillful Mao Asada's skating is!" once again when I saw her at this year's THE ICE. The direction of her skating may be a bit different from Kostner's and she has her own excellence.
There was a certain kind of turns that she showed in her exhibition program at the show. It reminded me of John Curry's first ever ice show as a pro-skater held in New York long ago. In the dark at the rink there was only one spotlight. He appeared in the spotlight from nowhere. Then he skated around the rink a few times and showed the turns of the kind which Mao did in her exhibition program.
Lori Nichol is the one who once learned skating under Curry and she's a choreographer of Mao. Curry told Lori to work on compulsory figures all the way. Some of what Curry taught to her are handed down to Mao. They are connected. Curry is such a great skater. What he taught to his student is handed down to a student of his student and what he taught is handed down through generations. Curry left a talent who is Lori. And the talent is choreographing programs for world's top level skaters.
I heard good reputations for Mao's exhibition program of this season as innovative and challenging. Since I've seen that kind of program from 1972, I'm not sure her program is actually innovative. What I can say is it's great to have someone in the current field who can do something close to the skating of old days. Especially, her steps in the end of the program is so skillful and I think you may say that's simply awesome.
For compulsory figures you need everything of knee bent and stretch, swings of your free leg, where to put your upper body's weight, and so on. After all compulsory figures are what a skater's body memorized, or in other words it's skater's sensitivity itself.
So, it's tough to teach it to someone else. We coaches try our best in teaching by words. Then we sometimes receive reactions like "And what happens?" from our students. It makes us feel "Done." No way we can say how much our students will be reworded in their scores by working on compulsory figures.
Finally I have a thing that I want to say. It doesn't mean you are unable to skate even if you can't do compulsory figures. While, if you have knowledge and skills in compulsory figures, surely it will be very helpful for your skating now and forever.
_________
I loved to read Mr Sato saying he understands to the hell that jumps are important to win and then he repeats "that said" "that said"

skating skills should not be forgotten and compulsory figures are very helpful for you. I kind of understood what Mao and Mr Sato are aining at showing in competitions. Fingers crossed for Mao's recovery from an injury in her left knee and she'll show her best performance before she retires.
Mao's EX number which is mentioned in the article:
https://www.youtube.com/watch?v=fPPAArR6HCU