It cuts both ways. USC has become tremendously more selective in the past 20 years and (to my surprise), competes with Harvard and Stanford in fundraising – something that will pay prestige dividends over the next few decades.
On the other hand, it still suffers from the “U of Spoiled Children” moniker for those who don’t follow higher education trends.
I expect that moniker to slowly die, assuming USC continues to ascend as it has been.