Also one could compare it to listening to a concert pianist playing Beethoven for example. Would you enjoy the concert if the pianist constantly hit wrong notes? It would certainly take away from the beauty of the music being played. Concert pianists srtive for perfection likewise figure skaters strive for that "perfect" or "clean" skate.
The difference, though, is that concert pianists are aiming, above all, to serve the composer and the audience.
It would make more sense to compare what they're doing to skaters performing in a show, although skating shows do not have the same prestige that competitions or piano concerts do.
In some contexts concert musicians will serve their own egos or competitive instincts by playing difficult cadenzas to showcase technical skills, and in those cases a wrong note might be more forgivable if its clearly a product of the risky difficulty attempted.
Skaters who are competing, on the other hand, are aiming to prove their superiority to the rest of the skaters in the combination of technical content and execution. That includes taking risks by including more difficult moves than can *reliably* be performed perfectly every time. That includes adding nuances to moves (e.g., upper body movements in step sequences or elsewhere that make the steps more difficult but also more expressive/artistic than they would be with neutral body positions) that increase the beauty of the performance when successful but also increase the risk of error. Also, ice is slippery. And gets cut up by previous skaters. Each skater needs to balance the need to include as much difficulty as possible to compete with others who will be doing the same with the need to minimize errors. There's no way to win if you play it so safe that there's no risk of failure.
Suppose there were a sport of competitive piano playing that gave points for both difficulty and style. Also suppose that the keys would be greased.
Players would need to devise the most difficult passages they could have a chance of executing successfully and expressively, possibly with extra points for varying the relationship between the player's body and the piano in creative ways, knowing that there was a good chance that their fingers (or other body parts) would slip. Do they play something simple and safe, knowing that other players will take more risks? Or do they take the risks and accept the likelihood of some wrong or missed notes?
That might actually an exciting competition to watch/listen to, and rewarding to the audience because of the excitement and the suspense as to *whether* each player would succeed in playing a "clean" performance. The sport might involve players composing their own passages (or hiring composers to provide them with passages that best highlight their particular skills), or they might use established pieces from the repertoire, but either way, the point of that sort of piano competition would not be about who best serves the composer's intention. Thus, it would be a lot less like existing piano competitions or concerts, and a lot more like skating competitions.