It measures a specific kind of abstract cognition, which isn't useful for all majors. Doing well on the math general GRE or the math section of the SAT is largely irrelevant to whether or not someone will succeed in a math program, for instance. Because a totally different sort of abstract thinking is required.
And nobody in admissions really cares about the general GRE anyway, unless the scores are abysmal. And I wager the SAT is treated the same way.