Which is why I agree with NC's statement "It is absolutely STUPID to have a timed sport where the only person who knows the time is the referee ..." Allowing an official the latitude to potentially determine the outcome is just plain wrong.
Actually, I think it's the same with football in this regard: Once a play in football starts, even if the clock expires during the down, we allow the play to continue. And if a foul occurs, we extend the game with an untimed down.
In soccer, if the offense is pressing to score, and they are within 30 or so yards from the goal, this is considered a 'play', and the referee allows it to continue. As long as the offense is attacking the net and not passing it back and forth to each other at the 30, they will be allowed to complete the play, which might include several shots. Once the defense gets the ball out of there, the game is called.
How is it so different? What if a football team starts a possession with time on the clock, let them finish the DRIVE, not just the PLAY if the clock is expired? In hockey or basketball let the team who has possession of the ball have a last PLAY instead of just a last SHOT? Once the defense gets the ball/puck, game over.
This would change the strategies in games quite a bit, but it wouldn't be unfair. It would just be different.