Yes, the SAT favors rich applicants who can afford to pay for (and spend time on) test prep. Unfortunately, rich applicants can also pay to boost whatever other signal is used by the admissions committee. Extracurriculars? Those violin lessons didn't pay for themselves! High School internship? Consider which families have the connections to find those opportunities. And now research papers...
I actually think standardized test scores are considerably less subject to bias than anything else!
IMO, the only actual solution is to specifically consider socioeconomic background as part of the admissions process. But everyone hates that because it feels unfair. And it is unfair, but that's the point—any system we come up with will be unfair, so we have to find the least-unfair one.