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Precisely. I remember my university taking 35% off the top of all grants for a lab that was 30 years old (hadnt been updated), and a sufficient but hardly cutting edge instrument room. The university was getting far more money than if the PI rented lab space at an incubator.
At my university, 44% of the overheads go to the general fund, 34% are used to support research in various ways (including startup funds for new faculty), and 22% goes to the administration. For grants with the normal 56% overhead rate, that means 16%, 12%, and 8% of the total.
Grant overheads are good for the university, because they mostly come with no strings attached. The university is free to spend them as it sees fit, rather than according to what some big important outsider says.