Tech jobs generally don't care, but traditional management and those tracks really care about that.

Because getting a job in those areas is about abstract abilities that can't be (somewhat) measured with code tests, technology signifiers, and tricky questions like tech interviews.

So a certain school is a "class entry cue" for such tracks.

Sure, but that first job is likely to determine the rest of your career, if your career path is somewhat traditional. So the school reputation would still have been quite important overall (especially if you wanted to aim high and get hired from a top employer right out of university).