> Public schools are generally very good about providing a variety of extra-curricular activities to keep students focused upon athletic and scholarly activities outside the classroom if the student is willing to participate.

I think you’re greatly underestimating how much the college admissions game has changed in recent years. For top universities (like the better UCs, Ivies, etc.), being, for example, president of a club in one’s high school is essentially irrelevant. The paths to admission consist of: (1) being a top athlete, (2) significant extracurricular achievement (meaning state/national accolades, founding a non-profit, etc.), or (3) extreme adversity.

You’re absolutely correct that the SAT rewards those with wealth and resources the most. But the absurd time and resource investment required of modern high-schoolers and their families to participate in extracurriculars in the way top colleges now demand is far greater a burden than SAT prep.