I don’t think musical sensibility matters much for today’s top scorers in the sport of figure skating. But for those pursuing the performing art known as figure skating…
As you mention, I have seen many BEAUTIFUL, ACCOMPLISHED ballet dancers with zero sense of the music. Many ballet teachers in America believe that musicality is an innate and unteachable quality; and yet music educators teach it systematically to millions of children (and adults), and dance students in European academies routinely study music as well. I would encourage every performing artist to study a musical instrument (including voice, drums, etc), and if needed find a local music teacher for the journey.
Dance does not require music — you can make beautiful figure skating just to the sound of your own blades (and you can probably compete with something quite minimal, maybe as little as a click track) — but dance DOES require flow emanating from an internal body rhythm. And we train that, most typically by working with music: we will practice the same figure (pattern of movement) faster or slower, keeping steady with the music in all cases, and working out where our body naturally wants to go faster or slower than the music. That is how we learn to perform an Axel jump or pirouette without hesitation. I do feel it’s harder to synchronize to music in figure skating, at least while trying to stay on circles of a certain radius.
Unique among dance forms, figure skating leaves behind a visual record, whereas most other forms of dance exist only in the present. Music is not at all required to appreciate the art left behind.
It is true that studying dance or music can help one become a better figure skating artist. But I would encourage anyone considering such study to embrace it on its own terms, and to forget that you are a figure skater while you are immersed in the moment. I have verified that practicing figures to place will help you balance better and give you greater ankle strength and control in the ballet studio. But wouldn’t you find it strange if dancers came to the rink with the attitude that they don’t really care about figure skating, they just want to become a better dancer? Consider how music or dance professionals view such attitudes from figure skaters…