I don't find that to be a particularly common pattern regarding tragedy in particular. I mean, I do find that most junior music selections are chosen to teach the athletes how to develop different strengths as performers.
But I think there is a lot more to the tragic performance tradition as a whole. There was quite a good post about the significance of portraying tragedy in Russian culture a couple years ago. Of responding to real-life tragedy via performance. As a form of tribute. I think the post might have been on FSU rather than here or I would try to search for it and try to link it. But it was a very thoughtful post and really easy to see why tragedy is such a significant part of Russian cultural tradition.
And, I would hazard a guess, also a large part of the reason it is such a significant part of skating tradition as well. Though the tragic storytelling tradition is certainly a huge part of many other cultures, as anyone who has been compelled to sit through a Greek Drama or 19th Century Spanish literature class can attest.