Having the shootout before the game would potentially open it up if it's tied late, since one team knows it will lose. It would get the people to their seats right away. Players would get regular "practice" at shootouts. Players might be looser since most of these shootouts will be "meaningless".
Interesting, not sure what to think of it. I seriously doubt it will be adopted (game start time, for example, will be unpredictable). But what do you think of it as an idea?