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Of course he completed the assignment far too late and begrudgingly, but he completed it — and we’re not scrawling many red pen marks in the margins of Mayor de Blasio’s plan to overhaul middle- and high-school admissions amid COVID.

Gone are middle-school entry screens; they’ll be temporarily replaced with random matching based on listed student preference, district by district. That’s a move at which some parents will surely chafe, as it’ll scramble the student bodies at prized sixth-through-eighth grade schools.

There was no alternative. With COVID rendering moot attendance records, nixing state standardized tests for a year and complicating grades for a second year running, no criteria can meaningfully and fairly sort fifth graders in 2021. That sorting — relying on fourth graders’ classroom and test-taking records to determine which middle school they go to — was questionable to begin with. As Brooklyn’s District 15 shows, doing away with barriers to entry can diversify hallways and classrooms in our racially segregated school system without much downside.

For high schools, some sorting by academic aptitude, interest and talent makes sense. So we give kudos to de Blasio for keeping on the calendar auditions for the city’s outstanding performing arts schools, albeit moving them online. And we give double kudos for his decision not only to maintain the admissions exam that determines entry into Brooklyn Tech, Stuyvesant, Bronx Science and other coveted high schools, but to expand testing sites to middle schools all across the city.

Finally, the mayor scrapped high school district preferences, which let certain campuses — the Upper East Side’s Eleanor Roosevelt is the most prominent example — prioritize nearby kids for entry. They can still pick and choose who they let in, just not by geography.

That will promote racial and socioeconomic diversity without compromising quality.