It's not just a question of potential.

Getting into Yale directly confers high status, and it is fairly well gated by other status-related tests: honors classes and private schools nudge you to learn the kind of thinking that does well on the SAT, not the kind of thinking that keeps you out of danger, as well as pushing you to AP exam prep classes; and access to extracurricular activities is gated both implicitly (by school choice) and explicitly by disciplinary measures for low-status behaviors. Rednecks like JD Vance are a tiny minority of the Yale entering class, and lower-status groups like illegal immigrants are as far as I know completely absent.

Also, I think the idea that there is something that it takes to be high status is incorrect. Social status is its own phenomenon with its own rules, and sometimes it's pretty random: you get a good job against the odds, or a good spouse, or you narrowly escape a disabling accident. You could argue that "what it takes" in such cases is luck, but graduating from Yale doesn't indicate that you will be lucky in the future, only of things that have happened before that.