It's not really that they did away with the Golden Goal, it was more of a failed (in their eyes) experiment. Pre '94 (probably not a coincidence that was the year the World Cup was in the US) there was no such thing as golden goal. Everyone seems to think that the golden goal would create more offense, when the opposite was true. Teams don't want to give up a fluke (or counter attack) goal, so they just sit behind the ball and play defense.
Not related to your post, but the others bashing shootouts, what is a better alternative? I don't think I've ever heard any good ones. More subs, removing players, golden goal, silver goal, corner kicks (someone on ESPN mentioned that yesterday) all have their disadvantages, just as a shootout does. A penalty kick, despite what people here and on TV think, is not an automatic goal. Nor is defending one pure guesswork. As a goalie, you can predict where a player is shooting based on the angle of their hips or planted foot. At the World Cup level, I'm sure they study tape on to find patterns. Just because the goalie goes the wrong way doesn't mean that it is a pure guess. That would be like saying a batter who gets fooled by a curve ball was just guessing that it'd be a different pitch.