Maybe because graduate students directly contribute to the university’s mission by teaching undergrads and “producing” research (both of which bring in $$$), while administrators seem to be purely a cost center, many of whom serve no useful purpose?

I mean, the grants that are being cut is the money that graduate students bring in. Less grant money -> fewer graduate students. In theory maybe it's possible to be more efficient like you're suggesting, but it's hard to see how the immediate response could be any different.