UCB and UCLA do not offer a lot of merit scholarships (they offer some, but anything significant should be viewed as a super-reach); their primary discounting is need-based financial aid for in-state students. Their high selectivity and resulting student strength and related prestige is mainly the result of the large population of the state of California relative to the size of each school. In terms of seats per population, a more comparable ratio to other states would probably need to consider the entire UC system as the “flagship”, although even UCM and UCR are more selective than the actual flagships in some other states, despite being seen as “less desirable” schools by most.
Arizona is unusual in that it has only three state universities for its relatively large population, so the “flagship-level” schools (ASU and UA) admit the full range of students who are considered college ready (note also that ASU is in what it by far the biggest metro area, putting a substantial part of the state population in commuting range). ASU also recruits out-of-state students as well, perhaps seeing a market opportunity to get California students (with just-ok academic credentials but wealthy parents willing to pay out-of-state tuition) who would rather go to a flagship type school (ASU) rather than a commuter-based CSU.