I don't think this analogy holds, because in piano competitions, you usually hear the "Moonlight factor" in the winner immediately, you mark him with a 10 and the rest gets 0 (other marks are usually given strictly formally); no further thought and no use watching the videos; technology cannot catch what makes a winner anyway.
Yes, that's true if you have a clear winner from the start. It won't be so clear cut if you have to award many prizes. Take the Chopin competition in Warsaw for example. In the 2010 edition, the jury used a very complex scoring system. Apparently, initially each judge scored each performance individually. When deciding the prizewinners, the jury took hours to deliberate. If you have so many eminent pianists (including strong characters like Argerich) discussing something so subjective as piano music, I don't see how they could come to any meaningful agreement between themselves without detailed reference to the players' performance. Given that in the course of the competition, each contestant would have played for hours, spread over a period of weeks (i.e. much longer than a football match), it is hardly conceivable that the jury could have remembered every relevant detail.
Also bear in mind that the jury often makes very minute distinctions between contestants. For example, in 2005, the Chopin jury decided to award one 1st prize, no 2nd prize, two 3rd prizes, two 4th prizes, no 5th prize, and one 6th prize. They must be supermen
to be able to do that without refreshing their memory of contestants' performances.