There are other tried and trusted methods. In the US, some sports have single-round elimination post-season formats but not necessarily single-game elimination. The best of three, five, seven, or other odd-numbers games dilutes the excitement of each game as the number of games increases. In Europe, there is a tradition of replays. Traditionally, in mid-January, a week or two after the big teams played their first game in the FA Cup, there would be a series of midweek replays. Teams from the lower tiers of English football saw the FA Cup at the path to fame and fortune. Fame came in the form of a giant killing. Fortune came in the form of gate receipts from playing one of the top teams in the land. If the first encounter ended in a draw. A replay was another financial bonus.
Replays were never win-win-win. They could be an unwelcome extra game for the bigger clubs. In 2022 the FA Cup replays of January are gone. Replaced by penalty kicks as the ultimate decider. The FA Cup replay suffered because of conflicting vested interests. A range of governing bodies add to calendar congestion while claiming to do so for the benefit of the game. Wait for the bi-annual FIFA World Cup! Players and their representative bodies complain about the demand on players, many rested for cup games, while accepting nest eggs provided by the golden goose.
There was a time in the 19th century when the FA Cup, with its single-round elimination format, was the premier competition in English football. However, the desire for fixity-of-fixtures resulted in a movement to a league format. The FA Cup survived but its prestige has diminished as its financial importance to the bigger clubs diminished. The replay has slipped away from the 2022 calendar. Will it return? Should it return?