I probably agree about test prep itself. But retaking the test, and taking both the ACT and the SAT (unless you know exactly where you're applying and hit your mark with one of the tests, which is something sophisticated families do but not everyone), is totally normal in high-SES households, and not normal in low-SES households. And that's just one SES-based detail; there are others (again: everything else they had to control for).
And, I mean, this kind of has to be true. Otherwise, you're ultimately going to get checkmated into arguing that low-SES working class folks are just genetically predisposed to do poorly on college entrance exams, which nobody believes.
Obviously, degree attainment tracks SES for other reasons: low SES prospective students have to be in a position to forego 4 years of income and job experience, as well as the prospect of moving away from their families to higher-SES areas in order to take advantage of the earnings potential of those degrees. But there are stark difference just in entrance exam scores themselves between high- and low-SES students (and between Black and white students, with SES fixed).
You’re using SES as a proxy for cultural factors. My uncle immigrated to Toronto and never managed to get a real job. He tutors kids in the local low income immigrant community in math. Those kids are prepping for standardized tests. By contrast, my wife’s mom lives in a lower middle class city on the Oregon coast. Most of these people have been in America for 200+ years, and they’ve been poor the whole time. They don’t study for the SAT. I’ve been utterly shocked at how blasé they are about their own economic status. The folks like my wife who are exceptional leave and go become high SES somewhere else. Many other kids are smart and just dragged down by the local culture.
I don’t think we understand structural poverty. I think in part that’s because we focus on income alone, and race, but not on factors like subculture. The secret to unlocking the mysteries of structural poverty involve figuring out why white people in Oregon or West Virginia are poor while folks like Mormons managed to build solidly middle class societies despite persecution and moving to the middle of nowhere.
As far as I can tell, most American kids don’t prepare for the SAT even with free or cheap methods. The cost of test prep seems like a red herring.