I think the size bloat is an intermediate step that gives the university tuition money (ugh) to finance its continued growth. But I do agree that the overall population is far too big - one criticism nowadays is that USC is a public school with a private school sticker price, and the housing shortage has irked me for a long time as I was one of the people bounced out as a student.
Beyond that, I don’t see USC becoming the “Stanford of Southern California” primarily because, as others have said, USC’s strengths center on the arts / entertainment and the professions, whereas REAL prestige in academia comes from cranking out Nobel Prizes, Fields Medals, etc. in traditional disciplines like philosophy and the hard sciences. That’s not USC’s wheelhouse, although in the case of philosophy in particular, USC has actually built a good department in recent years. However programs like the film school and the video game design program don’t weigh heavily in the minds of the people who rank universities overall, even as they are consistently recognized as the best in the world in those fields.
My frustration in that regard is that schools in general only deal with 2-3 (?) of the 7-8-9 (?) multiple intelligences. I was actually just up at Stanford a few days ago talking with some of their students about that, and Stanford’s offerings in the arts, for example, are a very sore weak spot with the university, whereas they’re a core strength of USC. Entertainment IS very intelligent and very intellectual, but not in ways that traditional schooling rewards. Test scores and whatnot get students a look but admissions to programs like the film school is based on portfolios and intangibles, unlike, say, Caltech, which does admissions pretty much exclusively by the numbers. In my experience in Hollywood (and it does seem similar among friends in Silicon Valley), half of the people graduated with honors from Harvard and the other half never finished high school. You can guess which half is more successful.
In terms of personalities, you could boil it down to Stanford being the class computer nerd while USC is the class clown or drama queen. They’re all manifestations of talent, but the supposition that computer programming requires intelligence and the performing arts don’t is something that’s always rubbed me the wrong way. In any endeavor, the best make it look effortless, and when you consume a movie in 90-120 minutes, that’s a project that’s typically taken a few hundred people at least 2 years to put together.