Parents won't let me apply to "non-prestigious" schools

They cannot be all that prevalent, since only a small percentage of them have kids with credentials that make admission to a “top 10” (or whatever in admission selectivity) college even a remote possibility. In California alone, about 77,000 Asian students attend the CSUs, and about 341,000 Asian students attend the community colleges (including Filipino students, who are reported as a separate category by CSUs and community colleges). Compare those numbers to the number of Asian students who attend “top 10” colleges.