How to fix the overtime system in the NFL

The current overtime system that the NFL is employing has been a topic that's been up for debate for a long time. With the latest playoff game in which the Minnesota Vikings did not have a chance to touch the football while the Saints made the game winning field goal, I thought of a compromise where teams will still maintain an advantage for winning the coinflip, yet at the same time the team that loses the coinflip might stand a chance.

*I'm going to say that I haven't done adequate research on whether this method might be feasible, and I'm not going to claim I'm the first one that came up with this idea. So if there is someone else that has already came up with this idea, my apologies.

The team that wins the flip will win the game if they score a touchdown. If a FG is made, the opposing team will have 1 possession to tie with a FG, or win immediately should a touchdown is scored. Assuming the team that wins the coinflip does not score on their first possession, all bets are off and first team that scores wins.

The reason I believe the implementation of the FG/TD rule would benefit the game, is that too often teams only need to drive the ball 30-40 yards (or less should they get a good kickoff return), and thus taking away alot of the excitement that comes with overtime. With this rule, this ensures that team must drive the ball all the way down the field, and thus have "earned" the win while still maintaining the advantage of winning the coin-toss under the current system.