They changed it a few years back, before that, the team losing the coin toss was only guaranteed a chance if they stopped the other team. The change made it so that even if the team winning the toss got a FG, the other team still get's a chance...but if you give up a TD on that first drive, then no dice. I mean there's really not much you can do to make it completely fair. You can't play a whole extra quarter, the games are draining, taxing and dangerous as it is.
One thing you could do, is let the kickers decide it. Start them each on their own 30 yard line, they each take turns kicking and then moving back 5 yards till someone missed.
Yea it's a fair point FL and also there are both sides to the game and defense is as important as offense.
Like you say have to settle a game somehow.