Changes the way the game is played while still giving this so called unfair advantage to the team who wins the coin toss. So if both teams get the ball regardless, the one who wins the coin toss will always chose defense, then not only do they know what they have to do, they now have 4 instead of 3 downs to do it in. Huge advantage. I would argue the exact same advantage currently given to the coin toss winner.

If you want to change it from a coin toss to some other way to determine first possession in overtime that may be the most fair way to do it. But a coin toss is literally 50/50 so I can’t think of a more fair way to decide who gets the ball first and the defense is allowed to stop them or hold them to a FG like what happens in most nfl overtime games since the rule change.