You get "white schools". Parents always want the best for their children and this predictably leads to full segregation. I am actually surprised how egalitarian and inclusive the US is when it comes to education!
In my view, there's a degree to which such lopsided admissions represent a greater Asian American cultural emphasis on education (good) coupled with a marginal standardized test score advantage produced by many hours of after-school test prep (bad). As repeated studies have shown, the advantage of e.g. SAT test prep courses is consistently relatively small, but enough of an edge to matter when you're looking at a ~10% admissions rate [2][4]. Not all applicants have parents who can afford or are aware of the value of such test prep, so it represents an uneven advantage. Crucially, this advantage is not inherently racial, but rather an artifact of culture, parental choice, and socioeconomic background. To mitigate this uneven advantage without completely eliminating merit-based admissions, a blurring filter e.g. random lottery might be applied to the top X% of test scorers.
And there is absolutely value in merit-based admissions. It makes these magnet schools what they are [5]. Despite their distorted demographics, it's what enables schools like Stuyvesant to still function as effective ladders out of poverty for many students:
>What makes these schools so good? The general consensus is the academic rigor. But what’s come out clearly in our interviews with Stuyvesant graduates is something arguably more important: a peer-driven expectation of achievement. What Stuyvesant does is take 3,000 pretty bright kids and put them in a building together. Then magical things happen. They push each other, they strive to be like each other, they learn from each other.
>Nearly all of these kids went to college, often selective ones, and most went on to do well professionally. The poorer students became middle or upper-middle class, and the middle-class students often did better than their parents. And they were happy—most (though not all) felt that Stuyvesant had had a big effect on their lives. For instance, Elizabeth Reid Yee, a white 1985 graduate who grew up poor in Greenpoint, Brooklyn, fully credits Stuyvesant with keeping her from a life of poverty.
[0] https://en.wikipedia.org/wiki/Thomas_Jefferson_High_School_f...
[1] https://en.wikipedia.org/wiki/Fairfax_County,_Virginia
[2] https://en.wikipedia.org/wiki/Stuyvesant_High_School
[3] https://en.wikipedia.org/wiki/Demographics_of_New_York_City
[4] https://www.thoughtco.com/are-sat-prep-courses-worth-the-cos...
[5] https://www.theatlantic.com/education/archive/2018/06/new-yo...
To paraphrase MLK "judged not on the colour of their skin but on the size of their parents' bank accounts". So many doors magically open to you when your parents have money.
To a significant extent, Asian American parents and students have shown that merit-based admissions _do_ work as a socioeconomic equalizer (see above Atlantic article). The problem as I see it is how to replicate this success among other demographics, including white Americans of middle and working-class backgrounds. Another part of the solution in my view is just making more magnet schools.
More likely, segregation happens because parents don't always want the best for their kids. A lot of it is simply self-segregation, driven by varying parental attitudes to education and the like.