That's the big question. In addition, when a professor gets a grant, the university takes a large chunk (40-60%) for overhead.
Anecdote: When I started as a postdoc recently, all new faculty and staff had orientation together. This was the middle of the semester, and there were about 20-25 of us. Of that group, there were no new professors (beginning of semester, wouldn't be unusual), 2-3 postdocs, maybe 5 facilities people (janitor, electrician, etc). Everyone else was administration/communication/finance/etc.
Universities, particularly large ones, are very, very, top heavy (with part of that due to compliance with regulations).
For the most part, both increased tuition and falling research grants are symptoms of the same underlying cause: reduced government support for higher education and R&D.
With fewer funds for education, tuition rises. But that tuition is filling in the hole created by a subsidy gap. Not increased research.