The research I have read on the subject concludes that SAT/ACT scores help to predict college academic success, but they don't have as much predictive power as the subset of high-school grades I mentioned. Maybe that's because college students today don't have to write as much and as often as students in the past. I know that the writing skills of the college grads I have observed in recent years aren't very good.
Just based on experience, first as a student and now as a Trustee, I don't see how a grade in an advanced high-school math course is going to predict whether someone is likely to write a brilliant thesis on Shakespeare. I graduated Magna Cum Laude in English at a very tough school. I knew certifiable geniuses who got Summa and couldn't balance a checkbook. We don't need people like that to balance a checkbook.
It takes both sides of a brain to build a civilization—and a student body.