Interesting conversation!
I’ll just add that applying to UCs is somewhat a default practice for high-performing students in California. Next up, for many kids, is then deciding which non-public schools also to apply to – that could include USC or not. So the idea that more HW students apply to UCLA over USC means merely that “California kids often apply to UCs – and why shouldn’t they at their bargain rates.” Plenty of students might apply to prestigious-and-inexpensive UCs but if not going there, would instead prefer to go away for school if they are paying for private tuition. So in that case, USC wouldn’t make sense to apply to. That’s not a diss on their prestige.
UCLA and USC are both large schools but they operate VERY differently in terms of class size, programs offered, etc. I have kids in both systems (UC and USC), and both offer amazing educations in different ways.