In recent years… 17% or so of the enrolled freshman class have been FirstGen… 21% or so of the enrolled freshman class have been Pell Grant recipients and deemed low-income by the federal government… 66% of all current undergraduates in total receive some form of financial assistance - either need-based grants or merit scholarships. Are there rich kids there at USC? Of course. Are there celebrity kids there at USC? Of course. Are such examples the norm or the majority? No… far from it.
USC’s goal is to craft a well-rounded and diverse freshman class comprised of those who actually have a strong affinity for or connection to USC but who also come from a variety of backgrounds. Clearly, USC is not simply looking to admit only those who can afford to attend such an expensive private school. They are super generous with financial aid and also offer merit scholarships as a means to compete for those quality applicants who may have to attend elsewhere without such an offering.
USC could aim to fill its entire circa 3K freshman class with only those with 99th percentile test scores and 4.0 unweighted GPAs, but they do not do so. In fact, they routinely reject 4K+ such applicants. USC could also only admit wealthy legacy applicants, but they do not do so. USC now routinely rejects 90% of all legacy applicants… including many from wealthy backgrounds. Your question seems to imply a goal for USC that is simply not in line with what USC is truly about or aiming to accomplish these days.