OK, but let me be the contrarian.
In the 1990 World Cup (pay attention to that year), there were four games that went to a penalty shootout, including BOTH semi-final games. Two of the games in the knockout stage were 120 minutes of kicking the ball around for a 0-0 result and hoping to convert one more penalty kick than the opponent. (I, of course, had grown up with a variation of this as British football was my first sport).
So a Mississippi redneck (and then some others) were complaining like this:
"You play a game, it ends in a tie, and you stop the game and decide which team can kick one more short shot than the other, it's the dumbest way to settle who's a champion I've ever heard of."
Me:
"Really? You think that's worse than a bunch of college football teams who don't play each other going through an entire season with non-football people voting one poll and coaches another, when they reach the final stage of the season the best teams almost never play one another, and after the games are played, the two polls VOTE - I said VOTE - on which team they THINK would beat the other one in a game that will never be played? At least in World Cup soccer for those flaws, they actually DETERMINE THE WINNER ON THE FIELD!!"
I said 1990.
Y'all remember how that one turned out in the poll vote?
Two flawed champions, a third team everyone thought was the best team but had lost twice, and one champion only because they were the sole unbeaten while the other had benefited from an officiating blunder, and the whole thing turned into an argument about whether common opponents or "but we played a tougher schedule" was a valid point.
I know that doesn't address overtime - but at least we don't get a tie and as flawed as all systems are, someone leaves the field a winner instead of some non-sports people VOTING them the winner.