Strike out Sotnikova from the list and my answer is yes.
I don't view competitive skating as a viable long term career, and given we are talking about competition only, then the OGM is the pinnacle of the competitive skating, no matter how people may want to downplay its importance bc their faves didn't earn one. History remembers OGMs and I rather not be remembered as a skater who had the long career and everything BUT the OGM.
It depends on whether your primary goal is results, or whether it develops to be more. Tara is the perfect example of one who wanted the result: she aimed for the OGM, got it, and was out. "History," as you say, or the official record, may remember Tara better than it remembers Janet Lynn. But many, if not most people who love skating disagree. I remember reading that Tara didn't even know who Janet Lynn was, because she didn't win OGM.
To compete at the top level, yes, they have to want to win, to have the heart of a competitor (although I think some are competing against themselves as much as against their competitors.) But I think the lucky ones are those who find and develop passion and motivation for other aspects. Peggy Fleming was a tomboy who wanted to skate because she could be graceful. And, eventually, she made her sport an art.
Ironically, Tenley Albright, Carol Heiss, Janet Lynn, Peggy Fleming, Dorothy Hamill, Linda Frattiane, Roslyn Sumner, Debi Thomas, and Kristi Yamaguchi all retired from competitive skating around the age of 19 (give or take a year).
And all of them did this right after their Olympic medal season. (Obviously not all gold medals)
Same competitive career path as the OGM's you listed.
A completely, and I mean *completely* different kettle of fish. Those skaters you listed skated in the "amateur" era. Which meant that if they earned ONE dollar from skating, they weren't eligible to compete. So in America, the parents had to foot the bill and it couldn't go on forever. It's significant that Michelle was the first one who had such a long career; the "Pro-Am" era came in 1998. In 1994, skaters who had already gone professional had to be given a special pass, you could reinstate as an amateur and compete. After that, the rules were changed, and Olympic-eligible skaters could make money.
Kristi Yamaguchi was 21 when she won the Olympics in 1992. But she and her coach were actually aiming for her to win the 1994 Olympics, when Kristi would be 23. They thought 1992 was going to be won by Midori Ito or Tanya Harding, because their 3Axels gave them the technical edge.
I find this interesting because I feel exactly the opposite way. I like the skaters with longer careers and many memorable programs the best. Artistry takes time to develop. And while it is disappointing to not get an OGM, or any Olympic medal, it is not the end of the world, if you have performed solidly for a while and have been at least in contention for one.
I loved Caro's skating last season, I thought it was really profound. Or Mao's when she briefly returned after Sochi. It felt like they still skate because they have something to say, something unique with a voice all of their own (how sappy

) even if they faced stiff competition for that podium.
Living the music, interpreting the music, performance values, giving to the audience, entertaining from the heart, artistry, being a conduit of emotion for the audience through movement, athleticism, acting, or just loving beauty, expressing joy. Giving happiness. Or, as Carolina Kostner said, simply skating for herself. There may be as many motivations, or combinations of motivations, for skating besides winning or placing as there are skaters.