Some of the things in the Olympics are questionably sports. And others are just another stop on the professional circuits.
Speaking as a Gen-Xer who is absolutely sick to death, in equal measure, of Shakespeare, The Beatles, Queen, Michael Jackson, The Simpsons, Family Guy, The Killing Joke, bad Gunnery Sergeant Hartman impressions, the word “mid” used to describe everything between 3-8 on the scale, and pretty much every goddam fandom ever, I very, very strongly feel that humanity should look FORWARD and not get hopelessly mired in what was relevant/interesting/fun/exciting/revolutionary in the distant past. Yes, I’m going to be the guy who defends things like beach volleyball, skateboarding, and surfing being added. Because they’re big right now, that’s why! Simple question: How exactly do you plan to sell tickets to a sculpting event, or an oil painting event, or a sketch drawing event, particularly when the fans will have to stay quiet for the entire duration of the event? (Unless the organizers feel like going full-on Phoenix Open, which is just about unthinkable.)
On a broader note, why does the Olympics have to be a sprawling smorgasbord in the first place? I think dropping old ideas like tug-o-war and standing high jump that don’t draw anymore is a perfectly good idea. In fact, I’d go a step further and exclude sports that are so big outside the Olympics that they carry little or no prestige in it. I have no idea how Olympic soccer ever became a thing, tennis was just plain stupid, and baseball was marginal at best.
Anyway, if you want a fine arts competition, the best thing to do is make one. No need to try to fit it into an already bloated 16-day schedule.
“Do you have something against classical flute?” asks Spoons, the classically-trained flautist. 
Naw, just kidding. Well, I am a classically-trained flautist, that much is true, but I do agree with your sentiment. The Olympics is for athletes, but it’s not for musicians, artists, and writers.
Fully agree. I see nothing wrong with an “Olympics of the Arts” which, while not part of the athletic Olympics, is a competition nonetheless. Sculptors and painters are given a period of time in which to render a subject; musicians are given music they’ve never seen and must play it after only a few hours of practice; writers must do a “flash fiction” contest like we used to do here. You’d never sell tickets for any of this, but we might get some interesting results from it.
Art competition is a weird concept. Even juried exhibitions are a strange beast when they award a winner. It’s not like there’s some set of rules that the artists are abiding by, and the only measure of success or failure is whether more judges liked the work.
I doubt they’d listen to me if they decided to do it, though. In turn, I’m fortunately not required to agree with their assessment of the submitted works.
The problem I have with that is that events that become popular quickly can also become passé very quickly. Ski ballet (sort of like figure skating on skis) was a demonstration sport at the Olympics in 1988 and '92, and was gone from all international competitions by 2000.
I like the Olympics to have a lot of continuity from one Games to the next. Breaking is being introduced this year in Paris. Are the competitors really the best possible break dancers in the world, aor are they just the ones who happened to be doing it when it became an Olympic event? Maybe some youngster who watches it will be inspired to train hard to be an olympian, but the eent will be removed before they get the chance.
I heard something on the radio yesterday about arts in the Olympics, and the music was the opposite of what you describe. Apparently the composers would write music, and the judges would only see the sheet music and not hear it performed before picking a winner.
Like ice skating and ice dancing were before they made it more objective.
I have no objection to new events being added to the Olympics, and old ones retired, so long as the new events can be (mostly) objectively scored (I don’t think there’s any sport where competitors and fans don’t complain about biased officials). I could maybe even be convinced to add non-athletic competitions, like esports or chess. But not art.
Figure skating used to have the competitors skate in perfect circles but they no longer do that, perhaps in part because it’s boring to watch?
Those were the figures that gave figure skating its name. It was never shown in the TV coverage, though.
Robot Arm - Wikipedia article on demonstration sports. Although a few did become official events, they were never meant to be part of any continuity. Personally I found ski ballet a nice change of pace, but I’m not surprised it didn’t catch on. Just too cutesy and niche, plus the issue of how many skiers bother to do it in the first place.
Now that they’re a thing of the past, I don’t see something as, well, static as fine art ever gaining a foothold again.