Should NYC school choice diversify school assignments to match applicant demographics?

Some commentators are concerned that features closely correlated with race, for example, can be used in computerized algorithms that don't explicitly use race (see previous two posts here and here). But below is a proposal that sees using features correlated with race as an advantage for achieving diversity in NYC schools, with a view towards making admissions look as diverse as applications.

Here's a report from FastCompany:

How to fix segregation in NYC schools? Let students hack the algorithm
A Nobel Prize winner’s algorithm helps decide which students are placed in which New York schools. A team of students is trying to upgrade it.

"Many of the most desirable, highest-performing schools have a gross disparity between the racial breakdown of who applies versus who eventually attends those schools.

"Data acquired from the Department of Education by IntegrateNYC through a freedom of information request and provided to Fast Company bleakly demonstrates this point. For instance, while white students accounted for one quarter of students who applied in 2017 to Beacon High School, 42% of that Fall’s freshman class was white. At Eleanor Roosevelt High School, 16% of applicants that year were black, yet less than 1% of admitted students were black.

"Part of the problem is that the education children receive from kindergarten to eighth grade is not equal. Students who live in more affluent, largely white neighborhoods have better middle schools, which better prepare students for high school entrance exams. Students from wealthier families are also more likely to be able to afford private test prep for their students. But the city’s current admissions process does nothing to correct this.
...
"The solution students came up with was to create a new matchmaking algorithm that prioritizes factors highly correlated with race such as a student’s census tract, whether they receive free or reduced-price lunch, and whether English is their second language. Such an algorithm would boost disadvantaged students higher up in the matchmaking process, provided they have already passed a school’s screening process."
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In NYC, school principals have a lot of agency in determining the input of the school matching algorithm, in the form of preference lists for their schools. The city (i.e. the NYCDOE) provides guidelines for schools. So another approach to achieving more and different diversity would be to provide different guidelines and requirements for schools, that would change the inputs to the matching algorithm (the schools' rank order lists of students), rather than trying to modify the algorithm. My guess is that this would be a more effective, nuanced, and flexible approach.