Imo ID is a sport as well as other FS disciplines because ISU has developed a sport discipline form of it. I see it as a sport. Instead of jumps, lifts etc ID just has it´s own demanding elements, rules and requirements different from the other FS disciplines. The difficulties in judging concern all disciplines in FS more or less.
This discussion brought to my mind a recent interview of Mikhail Kolyada whit a title: “Ideally, we all should strive to be like the ice dancers”. He thinks single skaters have a lot to learn from ice dancers. https://www.isu.org/figure-skating/figure-skating-news/interviews/11861-mikhail-kolyada?templateParam=15 . Single skaters are not automatically good ice dancers when they change to ID. I also remembered Tracy talking about this question in TSL interview a couple of years ago. She said it was finally Thorvill and Dean that made ID accepted as a sport. (In YT beginning around 12:35-)
I have not heard that the ballet community has ever tried to develop ballet to be a sport discipline in the same way as ID community though there are some ballet competitions. I guess they could take it further towards sport, organize Worlds, Europeans etc but is there any will to do it, I don´t know. In Ballroom dancing there are Worlds, Europeans etc but I am not aware have they ever applied for the Olympics. They could for sure. Synchronized Skating has applied a couple of times but has not been accepted. They had high hopes for Peking but were turned down again. The IOC said that one reason for the denial is that there are not yet enough Syncro teams all over the world.
And finally: Kolyada´s words about ID: "Figure skating is such a smooth sport, everything should look like a knife cutting through butter. You need to strive for being like the dancers. They are flying over the ice. Ideally we all should strive to be like they are. I watch the ice dancers, how they are doing all this, so softly how they stretch their legs and arms and it is all beautiful."