I love how people who don't watch the sport at all have these great takes on what would make it better.
Shootouts are absolutely a fair way to end a game that's deadlocked after two hours of playing. There's a huge amount of skill involved, and the "luck" of winning a shootout is no greater than the "luck" involved in winning a game 3-2. It's a sport of very fine margins: one badly-timed tackle, one shot that's a few inches off target, one moment of lapsed concentration, and the result is different.
Incidentally, this is why pro leagues don't have playoffs. The only safe way to ensure the title goes to the best team is to play several dozen games and see who comes out on top. Cups, including the World Cup, have always involved a lot of luck. There's room for both kinds of competitions.
Setting aside the fairness issue, shootouts are great drama. There's also no practical alternative. The odds of a goal getting scored goes down as players get more and more exhausted. Even by the end of added time, the game is often starting to become a farce. And the injury risk is serious.
Expanding the goal, as you suggest, would fundamentally change the game. People would be taking shots from very long distance because the keeper would not have the ability to cover the goal, and you wouldn't need to be an extraordinarily accurate shooter to score, whereas with a normal goal, only really excellent players can reliably score from outside the box. Everyone on the field would be bombing balls towards the goal. This would force the defense to play a very high pressure all over the field. It would not be recognizable as the same game, and it would be pretty ugly to watch.
There's also the technical problem of what an expanding goal would look like. You say we "have the technology," but it's really not that simple. Are there going to be sliding tracks around the goal? That could be dangerous. How are you going to keep the net taught at different sizes? Are you replacing the net? That could take time. Finally, is this equipment going to be widely available so that everyone can train on it?