The US has a peculiar culture where elite academic institutions are very much willing to limit their numbers of students, so it's not clear to me that they will in the long run control costs. Large, prestigious US universities have historically preferred funding more administrators over more students.

Those elite universities are less like schools and more like towns, so the focus is not just on teaching students but on maintaining a community. Sometimes that means protecting the people you have at the expense of people you haven't met yet. In many cases, "more administrators" translates to "better town services", so it's nor surprising to me the preference to cut enrollment.

>in [t]he long run they need students but can cut administrators.

Have you spoken to any professors lately?