I'm totally uninformed here, but why can't the other UC system members learn to replicate whatever is necessary in order to work towards having a reputation in the same league as UC Berkeley?
I'm not saying the other schools have no experts, just that it's a situation where talent tends to concentrate.
Well, they're not independent. You apply to the UC system and you get a decision back telling you which schools you've been admitted to. So the system is free to decide that one campus is better than another one and implement that decision by assigning better students to the favored campus and worse students to the disfavored one.
I believe that's how Berkeley ended up as the 'top' campus in the first place - it was the best one because it was supposed to be the best one. UCLA is different; it "worked its way up" via applicant preference, by having better weather and/or proximity to Hollywood.
It is quite possible (although unlikely) to apply to UC Berkley and UC Merced but only be accepted to UC Berkley.
It’s theoretically possible, but given that UC Berkeley is impacted in lots of places and Merced is under capacity everywhere, not plausible (actually, given certain system-wide guarantees, its far more likely to apply to Berkeley but not Merced and still get offered admission to Merced than to apply to Berkeley and Merced and get offered Berkeley and not Merced.)