I like that idea, Math, of considering what skaters did after their amateur careers. Dick Button also had a good criterion: that a great skater left skating better than it was when he/she came in. So despite the fact that Sonia Henie's skating looked old-fashioned by the 1970s, she advanced the sport in several ways, including doing more demanding jumps than ladies ever did. As a pro skater, she also made skating attractive to larger audiences, both with her films and with her live shows. Without Henie, one might argue that skating would just have been a niche sport like dressage, interesting mainly to the families of people who had the money to train for years. Similarly, Button also advanced the jumps, and then later he did a lot of impresario work as well as his commentating on TV. He increased audiences and educated them as well.That is always the most interesting question. What are the criteria? There is a difference between an "I won lots of medals" all-star and a "I gave exquisite performances" all-star. I am sure that pangtongfan would concede that Patrick Chan is the all-time "read the protocols" champion, but not so much the all-time "look at my on-ice performances" champion.
For me, I would give heavy weight to what the skaters accomplished after their days of amateur competitions were over. Sonia Henie brought figure skating to hollywood. Dick Button was Mr. Figure Skating for half a century. Kurt Browning and Kristi Yamaguchi were better as professional entertainers than as amateur competitors. Scott Hamilton was a better entrepreneur and impresario than a skater. And Michelle Kwan wins the lifetime achievement award in the category of overall Kwanliness.