What are reasons why tournament directors want you to notate in a chess tournament?
They just like being mean to little kids. 
Well, really, if there's a dispute about the game, the scoresheet can often be used to resolve the problem.
You should also want to record your games. How else can you study them so you can get better? Also, if you played another immortal game, would you want to deprive the chess world of that gift?
Notating is a necessity for any chess player. Without the use of proper hand-written notation, it is impossible to study your games and to learn from your mistakes. Notation should not be taken as a burden. Instead, it should be an opportunity to learn new things.
If your opponent makes an illegal move, how will you prove it?
If you draw by repetition, how will you prove it?
This sort of thing (even though others already mentioned it).
It's a rule, at least per FIDE.
----------
(p. 28)
ARTICLE 11. THE RECORDING OF GAMES
11.1 In the course of play each player is required to
record the game (his own moves and those of
his opponent), move after move, as clearly
and legibly as possible in the Algebraic
notation, on the scoresheet prescribed for
the competition. It is irrelevant whether the
player first makes his move and then writes
down the move on his score sheet or vice-
versa.
Kazic, Bozidar, Raymond Keene, and Lim Kok Ann. 1985. The Official Laws of Chess and other FIDE regulations. London: B. T. Batsford Limited.
It's a rule, at least per FIDE.
----------
(p. 28)
ARTICLE 11. THE RECORDING OF GAMES
11.1 In the course of play each player is required to
record the game (his own moves and those of
his opponent), move after move, as clearly
and legibly as possible in the Algebraic
notation, on the scoresheet prescribed for
the competition. It is irrelevant whether the
player first makes his move and then writes
down the move on his score sheet or vice-
versa.
Kazic, Bozidar, Raymond Keene, and Lim Kok Ann. 1985. The Official Laws of Chess and other FIDE regulations. London: B. T. Batsford Limited.
There's nothing like staying current, quoting from a 1985 rule book. 
You have nothing productive to offer? If not, then why criticize others? Do you really think FIDE would change a rule like that since 1985? Is 2014 recent enough for you?
https://www.fide.com/fide/handbook.html?id=171&view=article
You have nothing productive to offer? If not, then why criticize others? Do you really think FIDE would change a rule like that since 1985? Is 2014 recent enough for you?
Yes, I did have something productive, see my first post. The 1985 rule you posted is out of date. While you're still required to record the moves, the order of moving and recording is now important to FIDE.
You have nothing productive to offer? If not, then why criticize others? Do you really think FIDE would change a rule like that since 1985? Is 2014 recent enough for you?
And, while you ARE correct, it IS a rule, I suspect the OP was more interested in knowing WHY it is a rule.
What are reasons why tournament directors want you to notate in a chess tournament?