Two things to keep in mind:

1. Grants are difficult to get. The pay lines at both the NIH and NSF have been decreasing for quite some time, and even successful departments don't have the feeling of swimming in cash.

2. Overhead rates (the "tithes" you mention) do not necessarily cover the full administrative cost of a research-heavy department (especially things like capital construction).

There are certainly institutions that have built a great deal of monetary success on their research programs, but not as many as one might think. This is why, for example, in my field we're seeing a proliferation of MPH programs - student tuition is a more reliable income stream.

That's fair. Just that (again, my experience) you were charged a fixed amount in lab fees every semester regardless of courses. It's probably varies between unis.

> If you started treating departments as P&L centers, I don't know that I'd want to be in Anthropology vs. MechE.

I don't know if you need to treat each department as a P&L center. There are bound to be departments that are important but perennially loss-making and knowledge shouldn't be reduced to just dollars and cents. But there does need to be more fairness in the money charged to students. The alternative is that humanities students (with lower earning potential) are subsidizing STEM students (higher earning potential). I know which one I prefer from a fairness point-of-view (speaking as a former STEM student).