That strategy is not without flaws either: once you let the public decide you create a system where the incentive is not "who skates better?" but rather "who can play the audience better?". The EuroVision Song Contest, for instance, has a well-known issue where the public often votes for/against a singer not because of their song but rather because of geopolitics [1]. And that's before we discuss organized voting rings.
A related but less clear point is whether it's fair for the skater to be judged by people who have no idea about skating. If my code were to be negatively judged because (say) the person in charge judges the amount of comments rather than their content, I would probably be unhappy about that.
[1] https://en.wikipedia.org/wiki/Eurovision_Song_Contest#Politi...