Just from my observations as a fan of figure skating in Japan, here are some possible reasons why the sport is growing in popularity.
Is it correlation or causation, I don't know.
1. Champions or possible champions
Japan has several top level skaters who can be counted on (we hope) to take top placement in international competitions.
Not just one skater, but quite a few. Also, some very promising junior and novice skaters who the media also focus on.
It is not a cult of the individual.
2. Charismatic (for Japan) skaters
Skaters like Daiskue, Mao, Shizuka, Hanyu, Nobu, Akiko and even Machida have interesting personalities and charisma.
--Yes, they may seem very vanilla to you, but in Japan, they are seen as quite exotic. They don't follow the same rules as other Japanese in many ways.
And they are seen as good people. They are very careful of their image.
3. Media Coverage
The media covers all aspects of singles skating. Not just fluff pieces on the skaters but really in-depth explanations about the rules of figure skating.
After the 2014 World championships, a popular channel replayed Tatsuki and Hanyu's SP and LP with commentary about the GOE's of each of their jumps.
Before and after Sochi, there were many short pieces about the jump layout of Patrick Chan, Hanyu, Daisuke etc, and how that could impact the scores.
The Artistic elements are pretty much left to the individual to decide upon. They mention that someone like Daisuke has great expression and moves on ice like a dancer and leave it at that.
People know about the rules of figure skating and therefore can enjoy watching it more.
What about America and other countries where figure skating is in a decline? Can it be 'just' a lack of artistry that is causing this?