Per your post #13, but some of the questions from consulting and banking are undoubtedly geared towards those who are more analytical: “How many nickles could you lay across the state of New York to cover all of its square mileage?”
That’d be an unusual question, one undoubtedly given to catch the interviewee off guard, but someone more analytical could possibly have pondered this more naturally than your typical cookie-cutter business major. I think that’s why more UCLA students are gravitating to math and math/econ majors – because hopefully they are naturally more analytical. Even engineering and some other physical sciences besides math would seemingly be good also.
Re, your #14, you seem to me to be more about USC than UCB though, but that’s probably just because I brought some things up that (I thought) were questionable about USC’s admissions policy (the University possibly likening itself to Cornell notwithstanding). I do have respect for both UCB and USC, despite the latter’s admissions gaming attempts, with at least some of the mid-year admits occurring after space is freed at both USC and UCB.
One thing I didn’t bring up was that both USC and UCB are on the semester system, but they seem to have different credit hours. I believe that UCB has the standard 120 units needed to graduate at typically 3 units per class, but USC’s, if I remember correctly, have four-units/class. The link you provided for USC’s xfers – if I remember correctly – said that there were ~ 40 credits granted to the average xfer. If USC has a 128 credit threshold for graduation, that’d be ~ 1/3 of what’s needed. So USC is either chopping off a chunk of units, doubtlessly, but it’s also as you said undoubtedly taking some who are recent high-school grads.