Universities' top lines (revenue) consist of a few major areas: beyond tuition and any state aid (for state schools), research grants are a huge source of funding. Most of that comes from the federal government.
Most research grants have an itemized budget and, alongside the itemized budget, "indirect costs" that are often between 30-60% of the direct budget. Schools do, of course, have indirect costs associated with conducting research, such as facilities and actual administration (secretarial work, accountants, etc.). But these costs are not itemized and included in research grant budgets! It's just a percentage of the research budget.
Naturally, this both incentivizes institutions to maximize the size of the research budget and creates a large pool of nebulously-allocated money for rent seekers to try to socially capture.
At this point, I can't help but think that the federal agencies that write grants are somewhat complicit in this process.