The Summer Olympics alone has about 300 events that result in a gold medal followed by a gold, silver, and bronze medal presentation ceremony. For the drill, which has been repeated so many times on TV and other media, after the medals are presented, the organizer will raise the national flags of the three medalists and play the national anthem of the gold medalist's country.
It would be fresher if flag and anthem things could be scraped from the medal ceremony. I suspect the ancient Greeks didn't do it, and how many of us actually watch them anyway? I don't remember I ever watch any in full in the past 20 years. They are getting too old, and the audience are getting tired, mentally if not verbally. Who the medalists are will still be well known, since TV will still show all the information, including the national flags of the medalists, on the screen, and newspapers and internet will give you the same information and more. If you want to see the flags and hear the anthems, the opening ceremony will do. If you want to see more of the flags, the sports arena will display them, and the announcer can play the anthems randomly, just not every time somebody wins.
In addition to saving everybody time, this simplification will reduce the self-importance of sports and jingoism.