Around 20% of OT games end with a touchdown on the first drive. That's a significant enough percentage to have a minimum of one possession per team if you want the game to be decided on a fair basis.
If you don't like the hockey example, you can look at extra innings in baseball. What if they changed it so that first run wins and a coin toss is used to determine which team bats first instead of the usual away/home order.
I'm not a Green Bay fan, but it's now two years in a row they've been eliminated from the playoffs due to this rule. Think of all the time and effort put into the season to have it end like this. If you can easily make the OT rules more fair, why wouldn't you?