> My understanding (married to an academic) is that it's pretty difficult to get rid of tenured folksThis depends on the type of institution, but it's mostly a shared fiction on the order of "corporate culture". Ie, The sort of fiction that no leader dares to undermine when times are good but which goes out the window as soon as revenues start declining and cuts must happen.
At many institutions, there are no actual legal or contractual barriers to dismissing tenured faculty. Tenure is nothing more or less than a gentleperson's agreement. A social expectation.
Even where actual legal/contractual protection does exist, it typically protects the person's job but not the job itself. Ie, a university might not be able to fire a tenured professor and hire a new professor. But they can simply downsize the academic department and release the faculty member by virtue of the faculty position no longer existing. Maybe hire back ad junct labor a few semesters later if necessary.
> much easier to eliminate admin positions.
This largely depends on what you mean by "admin". Typically the split is between "staff" and "faculty".
The explosion of "staff" is not (just) a story of bloated middle management. It's also a story of the ongoing move from tenured to untenured labor. In particular: "staff" often includes people like instructors, ad junct teaching labor, research scientists, and post-docs.
Why would you fire an ad junct instructor or research scientist (staff) if they are cheaper than a professor (faculty) for roughly the same work?
In fact, a savvy financial engineer might even prefer the more contingent form of labor even though they are more expensive because a friction of releasing traditional faculty is expensive in terms of opportunity cost and agility.