NFL overtime rule. I'm sure I'm not the first one to have thought of it, but I don't recall seeing it before.
Historically, the NFL had a sudden death where a FG would end the game. They updated it in 2010 that if you kicked a field goal and were the first team to possess the ball, the other team had a possession. Up until 2017, it was a 15 minute period, where 2017 to today it is 10 minutes.
I would propose changing the rule to allowing both teams to possess the ball regardless of outcome of the first possession. I would keep the clock at 10 minutes and if the clock expires, the game is over, assuming one team leads another. The team receiving the ball has the opportunity to score. If they fail to score or kick a field goal, the other team can win the game with a TD (or field goal if the first team did not score). If the team possessing the ball first scores, they MUST kick the extra point. If the first team scores, the second team would then possess the ball with whatever time is remaining and must score before the clock hits zero. If they score a TD, they MUST go for 2. Should both teams kick a field goal in OT, we redo the coin toss, and the first team to score wins.