2.  Tests become easy.  DS took the SAT last fall to qualify for Johns Hopkins SET.  He found the 3 hour 45 minute exam "very relaxing", because that wasn't very long to concentrate, and he was allowed to take 3 breaks during the test.
This is only a result of chess if you don't love tests in the first place.
I always though that the SAT was a fun experience.
My point is slightly different.  Both DS & DD enjoy school and tests.  But when DD (who doesn't play chess) took the test a few years ago, she was very tired at the end.  DS was energized because it was fun and easy for him. 
I never had an interest in chess because it was extremely finite and struck me as somewhat boring.
Go is honestly probably a better game for what everybody is trying to accomplish here.
Perhaps chess is finite, but when you have to look 8-9 moves deep into a position to find the best move, visualizing the combinations is something I am incapable of, and something that my son has to think deeply about.
I've heard only good things about Go as well.