There have been nine NFL playoff games since the new rule which allows a team to walk-off the field with a touchdown on the opening possession.
2011 Broncos vs. Steelers Result: Broncos win on TD on 1st possession
2011 Giants vs. 49ers Result: Giants win on FG on 5th possession
2012 Ravens vs. Broncos Result: Ravens win on FG on 5th possession
2014 Seahawks vs. Packers Result: Seahawks win on TD on 1st possession
2015 Cardinals vs. Packers Result: Cardinals win on TD on 1st possession
2016 Patriots vs. Falcons Result: Patriots win on TD on 1st possession
2018 Rams vs. Saints Result: Rams win on FG on 2nd possession
2018 Patriots vs. Chiefs Result: Patriots win on TD on 1st possession
2019 Vikings vs. Saints Result: Vikings win on TD on 1st possession
Six of the nine games have ended on the 1st possession.
The longest was the Ravens/Broncos game, which lasted 16 minutes and 42 seconds (five possessions).
The quarterbacks who never got to touch the ball in Overtime:
Aaron Rodgers (twice)
If I was king of the world, I would have a 5th quarter, followed by sudden death, if still tied after 15 minutes.
The NFL must have already considered (and discarded) that idea.
Therefore, my next favorite idea is just a tweak on the current rule. And maybe it's something that would be considered.
I believe that a team should have to score not just a touchdown, but also a 2-point conversion if it wants to walk off the field after the first possession. That would have changed the above outcomes from six of nine ending with one overtime possession to, maybe, just three of nine.
That's a hugely more satisfying outcome.
Further, a coach would have a myriad of things to consider when he was confronted with the choice of whether to go for a 2-point conversion following a score on an overtime's opening possession.
One choice might be to just kick the extra point and let the overtime continue for at least one more possession (where you could only be BEAT) if the other team scored a touchdown and went for 2.
Certainly, the team which plays defense on the opening possession would almost always go for 2 on a second possession, if down seven points, lest it kick a game-tying extra point only to give the ball back to its opponent with the possibility of then losing on a field goal on the overtime's 3rd possession.
But, who knows? So much would depend on the teams and their personnel.
The strategic decisions would be fascinating.
But, more importantly, it would greatly decrease the current unfairness of the existing format, and level out the vagaries of a coin flip.
Just my thoughts...