Not too sure what the debate is here because a simple Google search will find cites which say that higher SAT scores by the student correspond to higher incomes later in the students life:
As well as cites which state that higher family income corresponds to students having higher SAT scores:
It’s not surprising that a child who has a family fortune of, say, $5,000,000 both (a) can concentrate fully on their SAT’s and (b) can be assured of a job paying 6-figures (work in the family biz), while a child who’s family has a $50k net worth (a) might be resource-constrained in the amount of time they have to prepare, and (b) may be conceptually-constrained in the idea that they are even worth a 6-figure job.
What I mean by that last is that success breeds success - Shea Serrano, a native San Antonian who became the first Latino writer to have three NY Times #1 best sellers, said that growing up on the Southside of San Antonio, the idea of a young Hispanic boy working for an American book publisher meant that you were working the warehouse. He notes that when he was raised, there was nobody who told him that instead of hauling the books, he could be the one writing them.
Your social milieu… much of which is stratified by wealth… has more to do with your future baseline success than your SAT scores, but your social milieu also impacts your SAT scores more than is given credit. A southsider in San Antonio thinking he has a future of hauling books will have a different attitude towards the test than a northsider wanting a future of writing them, and that, too, will reflect in the scores.