And they are primarily funded by outside, usually government, money that professors bring in through grants etc. If government doesn’t fund the professors, they can’t pay grad students. If they can’t pay grad students, then the university has to pay them directly from its own money, but the university can only pay so many grad students.

Through this whole thread, this is really the answer. Students don't just pay their own way. And the model isn't that universities give scholarships to PhD students. PhD students either get TAships (that are paid by the department) or RAships (paid by the professor through their research grants). If the school is losing (or at risk of losing) research grants then the first and easiest thing to go is grad students.

This isn't about administrative bloat or any of that other stuff. It's purely the model to fund grad students is being choked and this is one of the few levers programs have to adjust to it.