I say let them play one more full quarter. Heck let them play ten of them if they are still tied.
No, the basketball rule is even WORSE. Sudden death, it’s exciting, it’s fun, and both team HAVE a chance on every play. It’s not baseball, scoring is not asymmetrical. If you go basketball style then you wind up with the soccer problem of anti-climactic scoring. Imagine the lameness if after that amazing 80 yard throw and score now we have to wait another 14:45 to see if maybe the Steelers tie it back up or pull out a win. Part of what made that play great was that was it, game over the instant he crossed the end zone, not even kicking the extra point, do or die.
It’s still pretty much 50/50 with the team getting the ball first winning, because it puts pressure on the team with the ball to get first downs, or else the opponent will get the ball in good field position.