well, after playing for 120 minutes the players are usually exhausted,
and most of them have ran something like 10 miles, so making them play until someone scores sounds brutal, because that could last for several more minutes.
But both sides would be exhausted so it would be fair. Also most players in the World Cup tourney are professional level athletes, pretty they can take it. In baseball, they play inning after inning until there is a winner. In the playoffs, the NBA, NFL, and NHL all play their sport until there is a winner.
At least my way, the game would be decided by playing the sport itself instead of shoot outs.