While that might work in some cases, such a rule would be unfair in those parts of the world where extreme weather can occur.
If the extra time was played with strong winds and driving rain coming from one end of the pitch, the team with the wind behind them would have a clear advantage if the games was to be stopped when they scored after a few minutes. Playing the full 30 minutes ensures that each team has to play half the match with the wind behind them and the other half into the wind.