I may not have been clear, once the time runs out in the 4th quarter, 15 minutes is added to the clock, just in case nobody scores. But teams switch directions (like the end of any quarter). Once the "5th quarter" starts, its sudden death.
How does it not make it better? You aren't altering the natural play of the game or adding the advantage of a coin toss....just extending the game at the end of the 4th quarter, into sudden death. No coin toss, teams switch ends, but play continues the same way as between the 1st and 2nd quarters or the 3rd and 4th quarter, only now, it's sudden death. Only reason I said "add 15 minutes", is just in case nobody scores, you would still want to switch ends, in case the wind is an advantage.
The team with the ball at the end of the 4th quarter is in a tied game and possesses the ball in the natural course of the game. How is that an unfair advantage? I consider a team winning a coin toss and gaining possession that way, unfair.
Not sure why you are throwing in the notion "why not extend the first half too?" Are you just trying to be funny or does that in your mind change things in a positive way?