This is a complicated ecosystem, it's not that simple. Academic departments are not places where there's a lot of slack - positions are scarce, the competition

This is a complicated ecosystem, it's not that simple. Academic departments are not places where there's a lot of slack - positions are scarce, the competition for them is fierce, and the people who get them are notorious workaholics. Cutting admin means more work on professors, means less research output, means fewer grants funded, means fewer grad students supported. So you can cut students and get fewer students, or cut admin still get fewer students but also less research and funding as well.