Earlier quoted context omitted.
I don't really have evidence for this, but it's always felt like SAT/ACT coaching doesn't improve scores so much as get rid of some of the "dumb mistakes" that cost you score. It's gonna help you when the test writer was playing some gotcha tricks with phrasing or whatever, but if you don't understand the material, even narrowing it down to a 50/50 isn't going to get you a good score, and if you truly don't understan…
Coaching and studying improves SAT scores. People learn the type of questions they do poorly on and can study to improve. The SAT is a test you can study for.
It does miss something: in specific ethnic enclaves SAT coaching is much more effective, perhaps because of a culture of out-of-school schoolwork and teaching beyond SAT prep. Those enclaves aren't particularly wealthy either (if I recall correctly it was a Korean enclave). Even then we're talking 70 points -- not nothing, but also not a radical transformation.