I've always thought of artistic endeavors as more of a marathon than a sprint, which might be one reason you won't see any piano playing at the Olympics. It isn't that people haven't figured out how to make piano playing a competitive sport; they've just never been able to draw the ratings necessary for it. But imagine if they did put it on television.
For one thing, you would have to have a pair of announcers telling us all everything the pianist did that wasn't exactly up to par. You can't trust people to hear wrong notes themselves--I've made a career out of making mistakes that people are either too polite to point out or are too subtle for anyone without intimate knowledge of the score to hear in the first place. And when improvising, one can always take a missed note and make it sound intentional. It all depends on what you do in the moments immediately following.
And yet, in ice skating, it is completely obvious to anyone when someone falls on his or her can in the middle of a routine and yet you still have intermediaries crying out to let us know that it was a bad thing. Also, when a what was advertised as a triple axle turns out to be merely a double ("Bob, he's only playing that scale passage with one hand! That's an automatic deduction right there!") or when the landing was a bit wobbly ("that F# sounded more like mezzo forte than mezzo piano. We'll have to see what the judges think about that!"). There is no way NBC would let somebody get all the way through the Goldberg Variations without incessant commentary. People expect it.
(Actually, ABC tried presenting an entire football game on a Monday night in the 70s without announcers and they decided afterward people wanted them.)
But it's the pace of the arts that is the biggest obstacle, or perhaps the average attention span. This has apparently been compounded recently by the ubiquitous 90 second clips that festoon the online experience--it is rather difficult these days to actually watch a more lengthy excerpt. But, hey, the people have spoken (maybe).
But even on broadcast television you have to get through a sea of advertising. That's ok. For the longer events, say the marathon, they line up, the gun goes off, you see them run for thirty seconds, they go to commercial. They cover 3 other events. They go to commercial four times. They come back...people are still running! how exciting.
If the event is shorter, like a 3 minute skating program, they just stick commercials in between each of the competitors. I am old (and cranky) enough to remember when they would actually let you watch three or four people compete and THEN cut away to commercials. But, like all economic enterprises, people wanted to see if they could make just a little bit more money putting a few more ads in there which caused prices to come down which means they have to put more ads in there, and so forth.
I could imagine the day when piano made it to the Olympics (summer or winter, I wonder? I guess if it was a winter event you'd have to place it on ice.) On comes the Russian. He begins to play Chopin's "Minute" Waltz. Five measures of it. fade to a commercial for a car. We come back. Now he's playing part of the second section. We get another eight bars. Time for another commercial. Return for the big finish. And always the announcer telling us what we could have already figured out for ourselves, mostly. Heck, once in a while they say something I hadn't thought of, not being a retired competitor, and I learn something. Then he grins at the judges, takes a big bow, and walks off. We wait for the scores. Tears, or triumph. He moves into second place, for now. He gets flowers, and a hug from his coach. And his mommy. He waves at the camera. Such a cutie.
He is, of course, all of five years old.