“I think a lot of people want to live in Los Angeles, especially the Brentwood/Bel Air/Beverly Hills area, in which UCLA is nestled right in the middle”
No one in college or recent college graduates at UCLA are living in these areas, just too expensive. They may try to live in Santa Monica or the south bay but again very expensive. While Berkeley isn’t the best city to live in, the surrounding SF bay area including the east bay is very desirable to work and live.