I thought that the boards can register the moves electronically. What is the point of writing them down?
I can think of several reasons:
- The players will want to know how many moves have been played in the game (as you often get extra time after moves 40 and 60), how many moves have been played before the last pawn move or capture etc. Currently the players may not consult any other material than the score sheets during a game, but even if the rule was changed, the score sheet is probably the easiest way to access this information.
- The electronic boards can be unreliable sometimes. Also, although this probably never happens in Super GM level, problems may occur with illegal moves etc.
- There is no pressure to change the rules, or the trouble of changing the rules weighs more than the potential gain. Some players like the old-fashioned way of writing the moves down. Comparing with reason 2, somebody should decide when the electronic boards are good enough to be trusted, and drawing the line is not an easy job.
I'm not sure I understand the question properly. Are you suggesting electronic boards to print out the list of moves once the game is finished, so the players can sign it and save the time and effort to fill the scoresheets themselves during the game?
If you are proposing just to remove the scoresheet because there's an electronic register of the game, then I think the most important reason is that the scoresheets (because obviously there is one per player) are the only official documents, signed by both players, that attests that that game was played between those players and with the result that is noted on them (besides date, place, etc.). Eliminating this document would be like removing the signing of the wedding license because there's already a video of the ceremony.
The simple answer is because it is required by the FIDE competition rules.
The more complicated reason is that you cannot easily enforce other laws if you do not have your own written record.
It is a requirement to record all draw offers by writing "=" against the move when a draw offer is made. It is illegal to disturb your opponent by making repeated draw offers. If this happens the only way you can prove this is by means of the written score sheets. Draw offers are not recorded electronically.
Draw by 3-fold repetition. If you make an incorrect claim for a draw by 3-fold repetition your first penalty is to have your opponent given an extra 2 minutes on the clock. For a second offence you lose the game. A 3-fold repetition can unfold over many moves. It is not required that it take place over consecutive moves. The only way you can double check this to avoid a penalty for an incorrect claim is by examining your own score sheet.
Note that in a recent GM competition where because of the time controls (either rapid or blitz) the players were not required to record the moves the British GM Nigel Short wanted to claim a draw by 3 fold repetition but didn't make a claim because he didn't have a written scoresheet. He went on to lose the game and raised the point afterwards.
Note that in any case rule 6.13 states that: "Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made/completed, and clocks which also show the number of moves, are allowed in the playing hall. However, the player may not make a claim relying only on information shown in this manner"