That's exactly what TJ HS (top 1 HS in the US) tried to do to reduce their Asian representation, because Asians were "overrepresented".
Standardized tests are a better solution than "holistic" admissions, which bias heavily for students who can afford to go to expensive summer camps, competitions, and volunteer in poor countries. At least standardized tests can be studied for even if you're poor.
There are entire high schools in the New Orleans area whose average scores on standardized tests exceed all but 2-3 students at any public high school in the area. Having people with experience who know the answers because they can understand and teach the problem at a fundamental level is vastly better than any handout workbook.
Or they have kids whose parents have much greater respect for education and work ethic than other high schools.
I got a 99th percentile score on the SAT with just the typical prep books you find on Amazon (which I pirated) and self study and reflection on mistakes. If you keep blaming the system instead of holding people accountable for their own failures those underperforming high schools you mention will never become top scorers.
Standardized tests are a better solution than "holistic" admissions, which bias heavily for students who can afford to go to expensive summer camps, competitions, and volunteer in poor countries. At least standardized tests can be studied for even if you're poor.