It's harder to normalize performance across schools without a standardized test.
> those who placed in a state math competition are likely to have higher academic abilities
That sounds like a state-run math SAT that would have the same problems.
> And allow the wealthy to better position their kids at the detriment of the middle class.
The upper middle class is where it's actually interesting. There aren't enough wealthy people for the SAT to be a driver of mass inequality. They're already sending their kids to elite private schools, so as long as the Ivies keep favoring those schools, the status quo remains. The most important thing you can to to prepare for the SAT is do lots of practice tests. Those aren't that expensive. Anyone working class or higher can afford them. SAT classes help somewhat, but less than being somewhat familiar with the test. They're moderately expensive. Tutors are where it's interesting, and that's in upper middle class territory.
