I think what is so unique about Yuzu might be summed up like this: he has always been a person who makes 'what ifs' a reality. When he was younger, he was the embodiment of possibility, and now, in his prime, he is the greatest example of what happens when the potential of a remarkably talented young person is truly followed through on despite all the challenges lying in his way.
He has:
-Forced the scoring system to the breaking point
-Been one of the key players in facilitating the rapid technical development of the sport not just on the men's side but in women's and juniors as well
-Proven the value of being well-rounded with an excellent foundation, and showed what happens when a figure skater has the correct balance of fundamental technique, elements, and artistry, all at the highest levels; his competitors and good coaches of young skaters are studying his skating REAL HARD, I'm sure
-As a native son of an afflicted city and an athlete who is seen to embody the important Japanese virtues of resilience, humility, hard work and strength (just as the people of Tohoku were praised for their conduct after the disaster), has become a symbol of hope and triumph in Japan at just the time the country needed a boost in morale, and never stops using his position to draw attention to the cause of reconstruction. All the other Japanese skaters at the time of course did fundraising, charity shows, etc, but his personal connection runs deeper and makes his situation more poignant.
-Has single-handedly provided an economic and visibility boost to a 'fading' sport and to his city/prefecture, which is still in recovery (and, I'd venture to say, in wider Japan as a whole in certain ways). Wherever he goes, ticket sales and tourism dolla dolla bills (or whatever the local currency is) follow. Hanyuconomy! Hope the ISU has a plan in place for what they're going to do when he rees.
All that, plus a strong association with a cuddly icon everybody loves, an endearing sweetness and goofiness that offsets his shark-like competitive instincts, an open acknowledgment of his weaknesses and failures which keep him human and relatable and makes you root for him to succeed (he is great but he is not infallible, which makes him more intriguing and, I think, a better athlete), a personal life shrouded in mystery, a body like *chef kiss* (if y'all into that), and a face that fits very nicely with the current trends for young male beauty in east Asia, and you have yourself a phenomenon it is very easy to get emotionally invested in.