Where are you getting the quoted statistics from? The UC accountability report (https://accountability.universityofcalifornia.edu/2018/documents/pdfs/Accountability_2018_web.pdf) gives a breakdown of undergraduate income by campus and resident/non-resident in Fig 2.2.2 (page 47).
The data shows that UC wide, 38% of all families and 33% of resident families have income above $112K. At Berkeley, almost 50% of families have income above that level. That’s hardly being “shut out” when it’s roughly the 70th percentile of household income in CA (https://statisticalatlas.com/state/California/Household-Income). Only Merced matches the figures you cite, and I’d bet you’d see the same thing with community college too.