As someone who is (I think) on rayiner's side more or less, my impression of the evidence is that the SAT and similar tests (even IQ tests) can be practiced for to an extent, and scores can be improved, but only up to a "natural ceiling". So, while it should be possible for a while to improve everyone's scores on the SAT by providing test prep, you shouldn't expect everyone to be able to score near the upper limit on the SAT, just higher than they would be without test prep. Test prep has diminishing returns (unless that test prep is effectively cheating because the test questions and answers have been leaked) because the upper limit of a person's score is limited by their natural potential. The end state for the SAT, assuming the test isn't changed, is to produce a distribution more or less like a bell curve, but with a mean higher than before widespread test prep (and possibly some groups disproportionately improving compared to other groups, but not necessarily reaching the exact same mean as the other groups).
I'm not in favor of eliminating the SAT. I don't necessarily believe that SAT prep is materially impactful (I think it improves scores, but not, like, up a tier of selectivity). But all of the SAT improvement factors available to well-off families certainly do materially improve scores; those improvements include not just SAT prep, but also taking the test multiple times, having your results tracked by family and being forced to take the test multiple times, and disability accommodations, which are rampantly abused.
Low SES families are not taking the SAT on a level playing field with high SES families.