I understand that in some lower-level games, if the players do not record the moves, nobody else will do it for them. But what is the point of requiring the players at World Championship classical games to record the moves? After all, they can easily hire somebody else to do the job and let the players just focus on making the moves.
To my understanding there are a few reasons to require the players to record the moves. However, I believe that most of them could also be solved with a sufficient technological investment.
- Tradition: Chess has a rich history, and recording moves has been a part of the game for centuries. This tradition is preserved at the highest level to honor the game's roots and maintain continuity.
- Move Number Recording: A technical reason is that the players can easily keep track of the move number themselves that way, so that they know when they get the additional time at moves 40 and 60. The same argument could be made for three-fold repetition, which needs to be claimed instead of automatically taking effect, but I would suggest that it is not that easy to see from the record sheet.
- Legal Record Keeping: The fact that the physical record is signed by each party at the end gives it the semblance of a legal contract, which gives the players a sense of responsibility and fair play, although that argument is clearly weaker at the championship level, where this would be taken for granted anyway.
- Tier System Avoidance: At some level of professional play, the record keeping rule would need to be relaxed, introducing a tiered system, where one tier has to keep physical records and the other one does not. In general, many professional tournaments could then also relax the record keeping requirement, but at which level exactly would you then drop the requirement. Should the Candidates tournament, which is also very prestigious, drop the requirement? I think that ambiguity goes a long way in explaining the requirement.
I do not think that there are any technical reasons for maintaining the record keeping requirement. However, the sociological and convenience reasons lined out above probably pushed the arguments in favor of not dropping the record keeping requirement even for the world championship.
In addition to the answer already given, I would add:
To provide a paper-trail in case confusion or disputes arise.
There have been many cases of illegal moves or disputed moves during top-level play, especially involving the touch-move rule or during time pressure. For instance, the Kasparov touch-move incident against Polgar during the 1994 Linares tournament was a famous top-level incident.
In such cases, it can be helpful to have documentation of the game so far, according to the players themselves. Consider a situation where a piece is placed on the border between two squares, and a dispute arises between the players as to which square the piece was moved to. Having the players themselves document which square the piece was moved to provides a canonical record of the moves, which wouldn't otherwise exist.
This documentation is of peak importance in the highest-stakes games, where accurate arbitration of disputes is essential.