>faculty research overhead pays for department TAs

The majority comes from tuition budgets, which are assigned per credit-unit. This also pays for faculty salaries. Math is heavily dependent on tuition because they get little overhead. Life sciences is buying millions of dollars of equipment, chemicals, animals, lab staff that incur overhead, none in math.

>departments with rich professors maintain their TAs even through budget cuts

In fact the University of California does not get to keep any overhead. It goes right back into the State of California General Fund and the CA Legislature, as part of the budgeting process, decides where it goes (obviously considering where it came from). During a budget squeeze, overhead can be diverted elsewhere.

Because of this, for a number of years, it was unknown whether the research enterprise at the University of California was actually covering its overhead costs or operating at a loss.