Every day, when there is a shootout on the scorboard, I add an "ASAS" tag at the end of my comment. "Also, shootouts are stupid". From my standpoint, the regular season is about finding the best team over the course of the year, rather than finding a winner on a given night. If a game can't be figured out on a given night, then that's ok. It helps tell the story of the entire season, and a given game is just a chapter.
Baseball has extra innings, and basketball will go to as many overtimes as necessary, but football and hockey end it after a predetermined overtime period in the regular season. The games are physical and continued play could lead to an increased threat of injury, and regular season games just aren't worth it. Continued play, as is seen in the postseason, is an untenable solution to finding a winner.
It's not that I'm completely opposed to having a winner and loser every night. I want to make that clear. The real problem is that the shootout isn't a good way to end the games. Many people when berating the shootout say that it's like having a home run derby at the end of a baseball game, but I even disagree with that. You know, on a given roster, who is going to be able to hit home runs. The more players compete in a shootout, the clearer it is that shootout success is not a repeatable skill.
Of the top 30 active shootout goal scorers for their career, only two have a success rate of over 50%. TJ Oshie (52%) is pretty good. Franz Nielsen (54%) is not. Other than that, players that are used frequently in the shootout trend towards a success rate of less than 50%. Basically, you can throw your shooters out there, but that's not a guarantee of success. Sidney Crosby is a 41.8% shootout scorer. Alexander Ovechkin is a miserable 32.9.
You are playing a different game when you get to the shootout. Teams don't have a distinct advantage at any point during the shootout, and more weight is provided to games solved by what is essentially a coinflip (since they win 2 points, the loser receiving 1) rather than to teams who play the game of hockey the best. While I think it's unnecessary to have a winner and loser every night, it's even more asinine to determine the winner via a method that doesn't relate a tangible skill.