Let's not forget that many "great schools" are really cram academies for the SAT.
I've always understood the ACT as more about content and the SAT as more about aptitude, which means studying for the SAT is less useful than studying for the ACT.
You can teach test-taking strategies but those hardly require 2.5 years.
I agree some schools provide a better learning environment than others, and also engage in selective admissions either explicitly or via the socioeconomic status of the students' parents. Both of those could cause standardized test scores to improve but I wouldn't call it cramming.
Though this was some years ago, I took both ACT and SAT and found them almost identical.
I know SAT at least has added an essay section and otherwise moved away from multiple choice but still, to imagine you can't cram for it seems absurd.
In middle 70s, Federal Trade Commission investigated Stanley H. Kaplan, the big test prep company, over advertising that they could raise test scores. Well, investigation showed that yes, Kaplan could raise your SAT scores.
Like the College Board claims they can give approximately the same test for decades but somehow you can't study for it? Something doesn't seem right.
the SAT of the 70s were much more of an IQ test than now. I'd be surprised if Kaplan prep could raise more than 20 or 30 points on average.
Also, having used Kaplan's prep material... They're pretty bad. But that was in the early 2010s for myself so they might have fallen in quality.
IQ - you know IQ tests are renormed to reflect education levels, and raw scores mapped to give the bell curve?
So an IQ of 100 in 1900 would end up about 70 today. 70 oddly enough the number used to "prove" that people in the less developed world are inferior.
I took both in the early 1990s, 1430 SAT and 32 on the ACT, didn't study for either with exam prep.
For high school coursework I had AP Biology, Chemistry, Physics, and Calculus so from a content perspective I took all the courses you'd need to know things for both tests.
My understanding on the 32/36 and 1430/1600 is those are equivalent scores for the exams. I'm just one anecdotal data point so take it for what it's worth.
P.S. Studying for SAT felt like it would have had a bigger impact on my personal score. The analogy vocabulary section I did very poorly on (480/800). In my day they showed you your English score in two sections, vocab and reading comprehension (which I scored 800/800). Those 2 combined / 2 + math gave you your total.