My understanding of the research on predictors of academic success in college is that grades earned in challenging high-school courses (e.g., AP Calculus, science, etc.) are the best predictors, followed by SAT/ACT scores. Nothing else (reference letters, extracurricular activities, ...) matters.
For students who are talented in quantitative subjects, there's no question math-related courses in high school can be a pretty objective measure. But they only tell you about mathematical ability. A test like the SAT verbal, which measures reading comprehension and analogy recognition, is really the only way to estimate verbal ability if high-school letter grades aren't particularly objective—which, in humanities courses, they're not.
Essays sent in with the application can help, but it's good to have that verbal SAT indicator—which, like a grade in a high-level math course, is a quantitative measure—in this case, measuring verbal ability and reasoning.