I think your metric of a deficient high school is clearly lacking. My high school math class was taught by an actual mathematician with over a decade of research experience and it was highly skewed towards understanding and derivation instead of memorization. This was highly successful in making for better math students and the class was a statistical anomaly in performance - and since everything shown was proven in class, it was not necessary to memorize anything. Homework was really only to improve mechanical abilities.
I don't see how spending more time on memorizing formulas instead of actually understanding formulas, deriving them, and going above and beyond the high school curriculum would be a deficiency, and you would definitely be penalised in the SAT with such an approach over an objectively worse education where students are exposed to less math and more memorization. There is objectively no value to memorizing what amounts to trivia that you will then immediately forget.
That is to say, I strongly disagree that SAT prep is actually going to be just making you a better student, and we seem to both agree that it is strongly correlated to SAT score, while using such prep is correlated to SES.