I can't think of another sport where a "relationship to the audience" would be a scoring requirement. In most other sports, the audience entertainment typically comes from the suspense of who will win, and the appreciation of the technical skills needed to achieve the end result (eg. baseball involves pitching, batting, running, throwing, catching, and strategy).
I think this is important. I think that some sports fans can appreciate the suspense of who will win a skating competition as decided by difficulty and success of the risk elements like jumps. They can easily see whether a skater falls or stumbles, they can soon learn to tell the difference between 2, 3, or 4 revolutions in the air (especially with replay), and with a minimum of study they can learn the relative difficulty of the various jump takeoffs even if it might take longer to recognize them for themselves. And often times the success and difficulty of the jumps
are the deciding factor in determining the results of competitions. This was probably most often true in the 1990s (post-figures, pre-IJS), although there have certainly been exceptions.
Sports oriented-viewers who hate the idea of show business or subjective aesthetic perceptions infiltrating the world of pure sport would tend to think that only the difficulty and success of the technical elements, especially the big obvious risk elements, should determine the results. And to the extent that is true, they can enjoy skating as sport entertainment.
Arts fans who look at skating as a performing art and want the results to reflect the success of each program as entertainment or as a work of art would value presentation criteria, obvious quality of elements, and again lack of obvious visible errors.
So aside from the agreement that "no falls or major stumbles" is important, these two groups would have opposite opinions about what should be important in deciding competitions.
However, both these emphases ignore the technical fine points that require more detailed knowledge of skating to appreciate.
Since most potential fans do not already skate themselves, and many would not have access to even beginning figure skating lessons even if they wanted for reasons of location or finances or physical fitness, there will always be a problem for perceptions of the sport that many details that are very important to the practitioners are invisible to the unschooled viewer.
I think the federations (and TV networks who want to build interest in the sport) would do well to find fan-friendly ways to educate fans about technical details that are important in determining results. Instead of saying "Oh, fans will never understand, so either we should just ignore what the fans think, or else we should dumb down the rules to be obvious to casual viewers," I think that instead they should do a better job of inviting fans to think like insiders and appreciate what's going on.
However, it's a complicated sport with a number of built-in contradictions, so viewers who are looking for something simple to understand without much effort of their own may find it hard to get drawn in.
If the ISU/judges had their way, would they structure competitions like "Figures" had been, and instead have the audience buy tickets to the Gala for the entertainment?
I imagine that there is a range of opinions among officials as to whether to ignore audience interests and focus primarily on technical fine points or whether to emphasize the artistic possibilities of the medium that can be incorporated into competitive formats and/or cater to audience interests in order to attract outside money to the sport through sales of tickets, TV rights, and sponsorships. Probably there are some sticklers who would be happy to judge elements only on technical difficulty and quality only, but I expect that most would at least want to keep the program-to-music format and those aspects of presentation scoring that reflect mastery of technique.
And some judges would want to emphasize the artistic impression, because that aspect of figure skating is why they love skating more than, say, diving. But their impressions of programs would be informed by knowledge of skating technique and by a close-up view of the ice surface that fans in the cheap seats don't have access to.