There was a much discussed opinion piece after the 2010 Olympics by a professional dancer/dance critic/professor of dance who, I believe, was artist in residence at the University of Michigan at the time. She was flabbergasted that Yuna Kim won the competition over Mao Asada. Asada was the better dancer, and this artist gave a lengthy technical evaluation to support her opinion.
What the professor did not understand was that although Asada was the better dancer, Kim was the better skater. This was a skating competition.
I think the answer to your first question is that, indeed,
components like interpretation and choreography are evaluated differently in skating than in dance. Despite Dick Button

there is no provision in the CoP for pointing your toes or turning out your knee, and in singles I do not think that the judges care very much whether your tango moves are authentic tango when tango music is playing.
As for whether this disconnect alienates audiences, I don't see why it should. True, professional dancers might snicker to see a skater struggle to drag her leg up into a Biellmann position. But the general audience is more moved by grand music and pretty positions. General audiences liked to hear Liberace tickling the ivories to old show tunes as much as they do a renowned concert pianist interpreting Brahmes.
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